<PAGE>   1
                       SECURITIES AND EXCHANGE COMMISSION

                             WASHINGTON, D.C. 20549

                                 F O R M  10-Q

[X]     QUARTERLY REPORT PURSUANT TO SECTION 13 OR 15(d) OF
        THE SECURITIES EXCHANGE ACT OF 1934

        For the quarterly period ended October 3, 1998
                                       ---------------

        OR

[ ]     TRANSITION REPORT PURSUANT TO SECTION 13 OR 15(d) OF
        THE SECURITIES EXCHANGE ACT OF 1934

        For the transition period from________to_________

                          Commission File Number 1-313
                                                 -----

                 T H E  L A M S O N  &  S E S S I O N S  C O.
                 --------------------------------------------
             (Exact name of Registrant as specified in its charter)

              Ohio                                        34-0349210
---------------------------------------        ---------------------------------
    (State or other jurisdiction of            (IRS Employer Identification No.)
    incorporation or organization)

     25701 Science Park Drive
           Cleveland, Ohio                               44122-9803
---------------------------------------        ---------------------------------
(Address of principal executive offices)                 (Zip Code)

                                  216/464-3400
              ----------------------------------------------------
              (Registrant's telephone number, including area code)



        (Former name, former address and former fiscal year, if changed since
last report.)

Indicate by check mark whether the registrant (1) has filed all reports required
to be filed by Section 13 or 15(d) of the Securities Exchange Act of 1934 during
the preceding 12 months (or for such shorter period that the registrant was
required to file such reports), and (2) has been subject to such filing
requirements for the past 90 days. Yes   X   No
                                        ---     ---

                       APPLICABLE ONLY TO ISSUERS INVOLVED
                        IN BANKRUPTCY PROCEEDINGS DURING
                            THE PRECEDING FIVE YEARS:

Indicate by check mark whether the registrant has filed all documents and
reports required to be filed by Sections 12, 13 or 15(d) of the Securities
Exchange Act of 1934 subsequent to the distribution of securities under a plan
confirmed by a court. Yes     No
                         ---     ---


                      APPLICABLE ONLY TO CORPORATE ISSUERS:
As of October 3, 1998 the Registrant had outstanding 13,444,534 common shares.



                                      -1-

<PAGE>   2

PART I

ITEM 1 - FINANCIAL STATEMENTS


CONSOLIDATED STATEMENTS OF INCOME (UNAUDITED)
THE LAMSON & SESSIONS CO. AND SUBSIDIARIES


(IN THOUSANDS, EXCEPT PER SHARE DATA)

<TABLE>
<CAPTION>
                                                     THIRD QUARTER                  NINE MONTHS ENDED
                                                         ENDED                           
                                             ----------------------------     ----------------------------
                                                 1998            1997             1998            1997
                                             ----------------------------     ----------------------------
<S>                                          <C>             <C>              <C>             <C>
NET SALES                                         $73,160         $70,492         $209,122        $211,775
Cost of products sold                              57,885          62,139          167,215         175,757
                                             ------------    ------------     ------------    ------------

GROSS PROFIT                                       15,275           8,353           41,907          36,018

Selling, general and
administrative expenses                            11,305          12,954           34,233          36,247
                                             ------------    ------------     ------------    ------------

OPERATING INCOME (LOSS)                             3,970          (4,601)           7,674            (229)
Interest                                            1,059           1,046            3,438           2,686
                                             ------------    ------------     ------------    ------------

INCOME (LOSS) BEFORE INCOME TAXES                   2,911          (5,647)           4,236          (2,915)

Income tax benefit                                    700               0            1,400           1,400
                                             ------------    ------------     ------------    ------------

NET INCOME (LOSS)                                  $3,611         ($5,647)          $5,636         ($1,515)
                                             ============    ============     ============    ============

BASIC EARNINGS (LOSS) PER COMMON SHARE              $0.27          ($0.42)           $0.42          ($0.11)
                                             ============    ============     ============    ============

DILLUTED EARNINGS (LOSS) PER COMMON SHARE           $0.27          ($0.42)           $0.42          ($0.11)
                                             ============    ============     ============    ============

AVERAGE COMMON SHARES                              13,445          13,378           13,429          13,331
                                             ============    ============     ============    ============
</TABLE>

See Notes to Consolidated Financial Statements (Unaudited)




                                      -2-
<PAGE>   3

CONSOLIDATED BALANCE SHEET (Unaudited)


THE LAMSON & SESSIONS CO. AND SUBSIDIARIES
 (DOLLARS IN THOUSANDS)

<TABLE>
<CAPTION>
                                                                               THIRD                             THIRD
                                                                              QUARTER                           QUARTER
                                                                               ENDED          YEAR END           ENDED
                                                                            ------------     ------------     ------------
                                                                               1998              1997             1997
                                                                            ------------     ------------     ------------
<S>                                                                         <C>              <C>              <C>    
ASSETS
CURRENT ASSETS
        Cash and cash equivalents                                           $     1 ,449     $      1,410     $        382
        Accounts receivable                                                       43,940           32,951           43,937
        Inventories
         Finished goods and work-in-process                                       33,267           39,532           34,564
         Raw materials and supplies                                                5,394            6,043            5,549
                                                                            ------------     ------------     ------------
                                                                                  38,661           45,575           40,113
        Prepaid expenses and other                                                 9,193           11,631           11,763
                                                                            ------------     ------------     ------------
      TOTAL CURRENT ASSETS                                                        93,243           91,567           96,195

      OTHER ASSETS                                                                15,603           14,598           10,233

      PROPERTY, PLANT AND EQUIPMENT                                              113,469          111,211          119,995
      Less allowance for depreciation and amortization                            61,025           54,882           56,934
                                                                            ------------     ------------     ------------
                                                                                  52,444           56,329           63,061
                                                                            ------------     ------------     ------------

                                                               TOTAL ASSETS $    161,290     $    162,494     $    169,489
                                                                            ============     ============     ============
      LIABILITIES AND SHAREHOLDERS' EQUITY
      CURRENT LIABILITIES
        Accounts payable                                                    $     22,229     $     27,734     $     27,853
        Accrued expenses and other liabilities                                    23,342           22,272           21,951
        Taxes                                                                      3,663            3,815            3,473
        Current maturities of long-term debt                                       3,929            3,759            3,726
                                                                            ------------     ------------     ------------
      TOTAL CURRENT LIABILITIES                                                   53,163           57,580           57,003

      LONG-TERM DEBT                                                              44,936           44,712           48,126

      POST-RETIREMENT BENEFITS AND OTHER LONG-TERM LIABILITIES                    20,405           23,221           20,575
      SHAREHOLDERS' EQUITY
        Common shares                                                              1,344            1,341            1,340
        Other capital                                                             73,575           73,409           73,295
        Retained earnings (deficit)                                              (31,043)         (36,679)         (28,820)
        Other adjustments                                                         (1,090)          (1,090)          (2,030)
                                                                            ------------     ------------     ------------
                                                                                  42,786           36,981           43,785
                                                                            ------------     ------------     ------------
                                 TOTAL LIABILITIES AND SHAREHOLDERS' EQUITY $    161,290     $    162,494          169,489
                                                                            ============     ============     ============
</TABLE>

See Notes to Consolidated Financial Statements (Unaudited)


                                      -3-
<PAGE>   4

CONSOLIDATED STATEMENT OF CASH FLOWS (Unaudited)


THE LAMSON & SESSIONS CO. AND SUBSIDIARIES


(DOLLARS IN THOUSANDS)


<TABLE>
<CAPTION>
                                                                              NINE MONTHS ENDED
                                                                        ------------------------------
                                                                            1998               1997   
                                                                        ------------------------------
<S>                                                                     <C>                <C>        
OPERATING ACTIVITIES                                                                                  
  Net income (loss)                                                     $  5,636           $ (1,515)  
  Adjustments to reconcile net income (loss) to cash provided (used)                                  
  by operations:                                                                                      
    Depreciation and amortization                                          7,410              6,415   
    Deferred income tax benefit                                           (1,400)            (1,450)  
    Net change in working capital accounts:                                                           
     Accounts receivable                                                 (10,989)            (7,311)  
     Inventories                                                           6,914              2,709   
     Prepaid expenses and other                                            2,438               (298)  
     Current liabilities                                                  (3,887)             5,468   
    Net change in other long-term items                                   (3,416)            (6,758)  
                                                                        --------           --------   
CASH PROVIDED (USED) BY OPERATING ACTIVITIES                               2,706             (2,740)  
                                                                                                      
INVESTING ACTIVITIES                                                                                    
  Net purchases of property, plant and equipment                          (3,230)            (8,915)  
                                                                        --------           --------   
CASH (USED) BY INVESTING ACTIVITIES                                       (3,230)            (8,915)  
                                                                                                      
FINANCING ACTIVITIES                                                                                   
  Net change in secured credit agreement                                     993             11,183   
  Net changes in long-term borrowing and capital lease obligations          (599)              (618)  
  Exercise of stock options                                                  169                514   
                                                                        --------           --------   
CASH PROVIDED BY FINANCING ACTIVITIES                                        563             11,079   
                                                                                                      
INCREASE (DECREASE) IN CASH                                                   39               (376)  
Cash at beginning of year                                                  1,410                758   
                                                                        --------           --------   
                                                                                                      
CASH AT END OF THE PERIOD                                               $  1,449           $    382   
                                                                        ========           ========   
</TABLE>


See Notes to Consolidated Financial Statements (Unaudited)





                                      -4-
<PAGE>   5

                   THE LAMSON & SESSIONS CO. AND SUBSIDIARIES

                   NOTES TO CONSOLIDATED FINANCIAL STATEMENTS

                                  (UNAUDITED)


NOTE A - BASIS OF PRESENTATION

The accompanying unaudited financial statements do not include all of the
information and notes required by generally accepted accounting principles for
complete financial statements. In the opinion of management, all adjustments
(consisting of normal recurring accruals and changes in accounting estimates)
considered necessary for a fair presentation of the results of operations have
been included. Certain 1997 amounts have been reclassified to conform with 1998
classifications.


NOTE B - ACCOUNTING POLICIES

In June 1997, the Financial Accounting Standards Board issued Statement No. 130,
"Reporting Comprehensive Income" (SFAS 130) and Statement No. 131, "Disclosures
about Segments of an Enterprise and Related Information" (SFAS 131). Both
statements are required to be adopted in 1998. Currently, the Company's only
elements of comprehensive income are cumulative translation and pension minimum
liability adjustments. The Company plans to provide the SFAS 130 required
disclosures in its 1998 Consolidated Statement of Shareholders' Equity, however,
in the third quarter and first nine months of 1998 and 1997 the components of
comprehensive income (loss), other than net income (loss), were immaterial and
accordingly were not reported herein. SFAS 131 requires that disclosure of
annual and interim financial and descriptive information about reportable
operating segments be reported on the same basis used internally for evaluating
segment performance and the allocation of resources. SFAS 131 will be adopted in
the year-end fiscal 1998 financial statements.


NOTE C - INCOME TAXES

The difference in the third quarter and first nine months of 1998 between the
tax provision and the applicable statutory tax rate is due to changes in the
valuation allowance related to the tax benefit arising from prior year net
operating loss carryforwards.





                                      -5-
<PAGE>   6

Item 2 - MANAGEMENT'S DISCUSSION AND ANALYSIS OF FINANCIAL CONDITION AND RESULTS
         OF OPERATIONS

FOR THE THREE MONTHS AND NINE MONTHS ENDED OCTOBER 3, 1998
AND COMPARABLE PERIODS ENDED OCTOBER 4, 1997


CONSOLIDATED STATEMENT OF INCOME

Net sales in the third quarter of 1998 increased by $2.7 million, or
approximately 3.8%, compared to the third quarter of 1997. Overall volume in the
commodity rigid pipe products increased by 5.8% over last year's third quarter
but average selling price of commodity rigid pipe products declined 10.5% due to
lower PVC resin prices being passed on to customers. This sales decline was
more than offset by the 9% increase in sales of priority products, primarily
in the specialty extrusion, raceway systems, enclosure and electrical fitting
product lines. Sales for the first nine months decreased by $2.7 million or
1.3% from the same period last year. Year-to-date sales reflect a decrease of
$6.9 million primarily caused by an 8.4% decline in the average unit selling
prices of commodity rigid pipe products when compared to the prior year period.

The gross margin increased favorably by 76% to 20.9% in the third quarter
compared to 11.9% reported for the same period in 1997. This improvement was a
result of reduced PVC resin costs referred to above, increased utilization of
the Company's manufacturing plants, improved cost controls in both plants and
distribution centers and a shift in product mix to higher margin items. As a
result, gross profit increased $6.9 million in the third quarter of 1998
compared to the third quarter of 1997.

Selling, general and administrative expenses at 15.5% of sales were nearly $1.6
million below the 18.4% incurred in the third quarter of 1997. Increased selling
expenses were due to higher commissions paid as a result of increasing sales of
priority products, however these were offset by lower general and
administrative costs. For the nine-month period, selling, general and
administrative costs fell $2 million compared to a year ago, attributable to the
decreased sales level and more efficient administrative operations. The Company
recorded an income tax benefit of $.7 million in the third quarter, consistent
with the prior quarter.


CONSOLIDATED BALANCE SHEET

Accounts receivable increased approximately $11 million compared to year-end
levels due to a seasonally higher concentration of sales in the third quarter
period. Accounts Receivable Days Sales Outstanding (DSO) improved in the third
quarter of 1998 to 54 days as a result of stronger cash collections compared to
60 days in the prior year quarter. Inventories for the current quarter decreased
$6.9 million from year-end levels, and $1.5 million from third quarter of 1997.
These reductions are a result of lower PVC resin costs and better inventory
control. Prepaid expenses and other assets were reduced by $2.4 million
primarily due to the receipt of insurance proceeds from the 1997 fire at Dimango
Products. Accounts payable decreased $5.5 million from year-end and $5.6
million from third quarter 1997 primarily due to lower PVC resin prices and
improved cost control. Post-retirement benefits and other long-term liabilities
have decreased by $2.8 million as the Company continues aggressively to pursue
strategies which will mitigate these costs.

Long-term debt increased $.4 million in the first nine months due to the funding
of capital expenditures in excess of operating cash flow. The debt level is down
by $3 million from the same period in the prior year as the Company returned to
profitability and experienced better working capital turnover.


                                      -6-
<PAGE>   7

CONSOLIDATED STATEMENT OF CASH FLOW

Operating cash flow has provided $2.7 million through the third quarter which 
contrasts with the $2.7 million used in the prior year period. This is
attributable to the return to profitability and lower inventory levels.

The Company believes that it has sufficient credit available to support the
operating needs of the business and also fund capital projects. Alternative
financing opportunities continue to be evaluated consistent with the Company's
growth requirements.


YEAR 2000 COMPLIANCE

As is the case with most other companies utilizing information technology
systems in their businesses, the Company is in the process of evaluating and
addressing Year 2000 ("Y2K") Compliance of its information technology systems as
set forth below. These efforts are designed to identify, address and resolve
issues that may be created by information technology systems written using two
digits rather than four to define the applicable year. This could result in a
systems' failure or miscalculations causing disruption of operations, including,
among other things, a temporary inability to process transactions, invoices or
engage in other normal business activities.

In 1995, the Company began a comprehensive review of the operating systems which
underlie its ability to conduct daily business activity. Over the next three
years concluding in 1997, the Company spent in excess of $15 million to replace
its core business operations and communications software systems; virtually all
of the computer and telecommunications hardware; and reengineered or adopted
best practices throughout its business process activities. The primary impetus
for this investment was to support the attainment of strategic business
objectives and to address Y2K concerns concurrently. This investment included a
significant commitment to electronic commerce activities with our customers and
manufacturers sales representative organizations. In addition, the Company has
implemented extensive education and skill development programs to provide for
continued knowledge transfer, ongoing support and functionality development.

During 1998, the Company authorized an independent audit of all software and
facilities equipment at each of its business sites to identify potential areas
of exposure, representing a continuing pro-active investment in addressing Y2K
concerns. As a follow-up to this audit, a Y2K cross-functional team was formed
to monitor and assess official compliance statements from our software and
equipment vendors and to initiate remediation activities at the non-compliant
sites where there could potentially be a material impact on our business. In
addition, the Company has contacted our significant customers and suppliers to
inform them of our compliance status, to determine their state of readiness and
to identify any subsequent actions which may be needed by us.

Current analysis indicates that our core business information system, to the
best of our knowledge, is Y2K compliant. As we address potential areas of
non-compliance, we are evaluating and prioritizing them on the basis of their
materiality to our business. We are utilizing existing staff in the respective
functional areas to assist in this evaluation process and take appropriate
corrective action, but we do not expect to incur significant additional costs
based on what has been identified to date. We will continue our compliance
investigation and develop contingency plans where necessary. We plan to complete
the


                                      -7-
<PAGE>   8

assessment phase by end of second quarter 1999, and expect to achieve Y2K
readiness on our internal computer systems and facilities equipment by end of
third quarter 1999.

While the information we have received regarding third-party systems, on which
the Company's systems rely, indicates that they are or will be Y2K compliant, we
cannot guarantee this, nor can we estimate at this time any material effect on
our Company and its operations if this would not be the case. The Company
continues its aggressive assessment of these potential third-party exposures and
will address the issues accordingly.

However, our ability to achieve these dates may be impacted by (i) the timely
availability of software patches by existing suppliers of software, (ii) the
Company's ability to employ and retain qualified professionals to handle Year
2000 issues, (iii) the ability of third parties to complete their own Year 2000
compliance remediation efforts on a timely basis, and (iv) the Company's
ability to prepare and implement contingency plans.


OUTLOOK

The Company experienced better product mix in the third quarter of 1998 as it
continued its efforts to improve profitability. Construction spending, new home
sales and retail sales trends appear to be steady heading into the last quarter
of 1998. The Company continues to make progress in attracting new customers,
improving operating efficiencies in its distribution network and increasing
utilization of manufacturing facilities. Based on these factors, and continued
moderation in PVC resin costs, the Company expects improvement in gross profit
and net earnings for the remainder of 1998 compared to 1997.

The Company should experience favorable operating cash flow and lower debt
levels in the fourth quarter due to improving working capital management and
seasonal factors. Increased capital spending is expected in the last quarter of
1998 and into 1999 to support additional capital spending requirements and
improved manufacturing and distribution efficiency. However, capital spending
will remain at a lower level than experienced in either 1996 or 1997.

As previously announced, the Company is conducting an evaluation of the
strategic alternatives available to reduce its exposure to highly volatile raw
material pricing as it relates to commodity sensitive PVC pipe products. This
evaluation process is continuing.

Statements under the captions "Year 2000 Compliance" and "Outlook" contain
expectations that are forward-looking statements within the meaning of the
Private Securities Litigation Reform Act of 1995. Actual results may differ
materially from those expected as a result of a variety of factors such as
(i) the volatility of polyvinyl chloride resin pricing, (ii) changes in the
pattern of construction spending in both the new construction, and repair and
rehabilitation markets, (iii) changes in the number and distribution of housing
starts, (iv) fluctuations in the interest rate affecting housing starts,
(v) unpredictable technological innovations that could make the Company's
products comparatively less attractive, (vi) changes in local, state and
federal regulations relating to building codes and the environment (in each
case as they may affect the attractiveness of the Company's products and
manufacturing costs), (vii) the ability of the Company to pass through raw
material cost increases to its customers, (viii) a reversal in the country's
general pattern of economic stability affecting the markets for the Company's
products, and (ix) the risk factors described in the last two paragraphs
under the caption "Year 2000 Compliance" and other potential unforeseen
Year 2000 compliance issues.


                                      -8-
<PAGE>   9

PART II

ITEM 6 - EXHIBITS AND REPORTS ON FORM 8-K

         (a)      Exhibits.

                  11  Computation of Earnings Per Common Share

                  27  Financial Data Schedule

         (b)      Reports on Form 8-K. There were no reports on Form 8-K filed
                  for the three months ended October 3, 1998.






                                      -9-
<PAGE>   10

                                   SIGNATURES


Pursuant to the requirements of the Securities Exchange Act of 1934, the
Registrant has duly caused this report to be signed on its behalf by the
undersigned, thereunto duly authorized.




                            THE LAMSON & SESSIONS CO.
                            -------------------------
                                  (Registrant)




DATE: November 17, 1998            By /s/    James J. Abel
      -----------                     -----------------------------------------
                                         Executive Vice President, Secretary,
                                         Treasurer and Chief Financial Officer









                                      -10-