<PAGE>   1
                       SECURITIES AND EXCHANGE COMMISSION

                             WASHINGTON, D.C. 20549

                                    FORM 10-Q

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

        For the quarterly period ended July 4, 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
                                                 -----

                           THE LAMSON & SESSIONS CO.
             ------------------------------------------------------
             (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 July 4, 1998 the Registrant had outstanding 13,444,484 common shares.


<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>
                                                         SECOND QUARTER           FIRST HALF
                                                              ENDED                  ENDED
                                                     ---------------------   ---------------------
                                                        1998        1997        1998        1997
                                                     ---------------------   ---------------------
<S>                                                   <C>         <C>         <C>         <C>
NET SALES                                             $71,168     $72,439     $135,962    $141,283
Cost of products sold                                  56,794      59,667      109,330     113,618
                                                      -------     -------     --------    --------

GROSS PROFIT                                           14,374      12,772       26,632      27,665

Selling, general and
 administrative expenses                               11,481      10,664       22,928      23,293
                                                      -------     -------     --------    --------

OPERATING INCOME                                        2,893       2,108        3,704       4,372
Interest                                                1,242         833        2,379       1,640
                                                      -------     -------     --------    --------

INCOME BEFORE INCOME TAXES                              1,651       1,275        1,325       2,732

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

NET INCOME                                            $ 2,351     $ 1,975     $  2,025    $  4,132
                                                      =======     =======     ========    ========

BASIC EARNINGS PER COMMON SHARE                       $  0.18     $  0.15     $   0.15    $   0.31
                                                      =======     =======     ========    ========

DILUTED EARNINGS PER COMMON SHARE                     $  0.17     $  0.15     $   0.15    $   0.31
                                                      =======     =======     ========    ========

AVERAGE COMMON SHARES                                  13,538      13,542       13,531      13,544
                                                      =======     =======     ========    ========
</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>
                                                          SECOND QUARTER                                  SECOND QUARTER
                                                               ENDED                    YEAR END              ENDED
                                                        ---------------------      -----------------    ------------------
                                                                1998                     1997                  1997
                                                        ---------------------      -----------------    ------------------
<S>                                                          <C>                      <C>                   <C>
ASSETS
CURRENT ASSETS
   Cash and cash equivalents                                 $    848                 $  1,410              $    556
   Accounts receivable                                         43,197                   32,951                48,701
   Inventories
     Finished goods and work-in-process                        35,015                   39,532                38,549
     Raw materials and supplies                                 4,854                    6,043                 5,544
                                                             --------                 --------              --------
                                                               39,869                   45,575                44,093
   Prepaid expenses and other                                   9,679                   11,631                10,939
                                                             --------                 --------              --------
TOTAL CURRENT ASSETS                                           93,593                   91,567               104,289

OTHER ASSETS                                                   15,373                   14,598                10,403

PROPERTY, PLANT AND EQUIPMENT                                 112,486                  111,211               119,860
Less allowance for depreciation and
     amortization                                              58,936                   54,882                56,654
                                                             --------                 --------              --------
                                                               53,550                   56,329                63,206
                                                             --------                 --------              --------

                               TOTAL ASSETS                  $162,516                 $162,494              $177,898
                                                             ========                 ========              ========

LIABILITIES AND SHAREHOLDERS' EQUITY
CURRENT LIABILITIES
   Accounts payable                                          $ 21,264                 $ 27,734              $ 25,086
   Accrued expenses and other liabilities                      22,791                   22,272                20,406
   Taxes                                                        3,640                    3,815                 3,724
   Current maturities of long-term debt                         3,799                    3,759                 3,626
                                                             --------                 --------              --------
TOTAL CURRENT LIABILITIES                                      51,494                   57,580                52,842

LONG-TERM DEBT                                                 49,951                   44,712                51,379

POST-RETIREMENT BENEFITS AND OTHER LONG-TERM
LIABILITIES                                                    21,897                   23,221                24,405
SHAREHOLDERS' EQUITY
   Common shares                                                1,344                    1,341                 1,332
   Other capital                                               73,574                   73,409                72,864
   Retained earnings (deficit)                                (34,654)                 (36,679)              (22,894)
   Pension adjustment                                          (1,090)                  (1,090)               (2,030)
                                                             --------                 --------              --------
                                                               39,174                   36,981                49,272
                                                             --------                 --------              --------
                               TOTAL LIABILITY AND 
                               SHAREHOLDERS' EQUITY          $162,516                 $162,494              $177,898
                                                             ========                 ========              ========
</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>
                                                                                              FIRST HALF ENDED
                                                                                 ------------------------------------------
                                                                                       1998                      1997
                                                                                 ------------------------------------------
<S>                                                                                 <C>                       <C>
OPERATING ACTIVITIES
   Net income                                                                       $  2,025                  $  4,132
   Adjustments to reconcile net income to cash (used) provided by
   operations:
      Depreciation and amortization                                                    5,038                     3,771
      Deferred income tax benefit                                                       (700)                   (1,450)
      Net change in working capital accounts:
        Accounts receivable                                                          (10,246)                  (12,075)
        Inventories                                                                    5,706                    (1,271)
        Prepaid expenses and other                                                     1,952                       526
        Current liabilities                                                           (5,776)                    1,686
      Net change in other long-term items                                             (1,946)                   (3,004)
                                                                                    ---------                 ---------
CASH USED BY OPERATING ACTIVITIES                                                     (3,947)                   (7,685)

INVESTING ACTIVITIES
   Net purchases of property, plant and equipment                                     (2,062)                   (6,309)
                                                                                    ---------                 ---------
CASH USED BY INVESTING ACTIVITIES                                                     (2,062)                   (6,309)

FINANCING ACTIVITIES
   Net change in secured credit agreement                                              5,435                    13,924
   Net changes in long-term borrowing and capital lease obligations                     (156)                     (206)
   Exercise of stock options                                                             168                        74
                                                                                    ---------                 ---------
CASH PROVIDED BY FINANCING ACTIVITIES                                                  5,447                    13,792

DECREASE IN CASH                                                                        (562)                     (202)
Cash at beginning of year                                                              1,410                       758
                                                                                    ---------                 ---------

CASH AT END OF THE PERIOD                                                           $    848                  $    556
                                                                                    =========                 =========
</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 and 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
         second quarter and first half 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 second quarter and first half 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 SIX MONTHS ENDED JULY 4, 1998
AND COMPARABLE PERIODS ENDED JULY 5, 1997


CONSOLIDATED STATEMENT OF INCOME

Net sales in the second quarter of 1998 decreased by $1.3 million, or 1.8%,
compared to the second quarter of 1997. The decline reflects an approximate 4%
reduction in average selling prices of commodity rigid pipe products with a
slight volume increase compared to second quarter 1997. The price reduction was
a result of polyvinylchloride (PVC) resin material cost decreases experienced
during the first half of 1998. This impact was offset by a 20% increase in
priority telecommunication product sales and an 18% increase in the large
diameter sewer pipe sales. Finally, the Company's wireless electrical products
business generated $1.2 million of sales in the second quarter of 1998 after
being immaterial in the same period of 1997 due to the Brighton, Michigan fire.
These additional sales helped to offset reductions from discontinued product
lines. Sales for the first half decreased by $5.3 million or 3.8% from the same
period last year.

Gross profit increased $1.6 million in the second quarter of 1998 compared to
the second quarter of 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, the gross margin
ncreased by 14.8% to 20.2% in the second quarter and compared favorably to
17.6% for the same period in 1997.

Selling, general and administrative expenses at 16.1% of sales were nearly $.8
million above year-ago levels in the second quarter. Increased selling expenses
were due to higher commissions paid as a result of increasing sales of priority
products. For the six-month period, selling, general and administrative costs
fell $.4 million compared to a year ago, attributable to the decreased first
half sales level. The Company recorded an income tax benefit of $.7 million in
the second quarter, consistent with the prior-year period.


CONSOLIDATED BALANCE SHEET

Accounts receivable increased approximately $10.2 million compared to year-end
levels due to a seasonally higher concentration of sales in the second quarter
period. Accounts receivable decreased by $5.5 million compared to the second
quarter in 1997 due to improved collection processes. Inventories for the
current quarter decreased $5.7 million from year-end levels, and $4.2 million
from second quarter of 1997. These reductions are a result of lower PVC resin
prices and better inventory control. Prepaid expenses and other assets were
reduced by $2.0 million primarily due to the settlement of an insurance claim
and receipt of proceeds from the 1997 fire at Dimango Products. Accounts payable
decreased $6.5 million from year-end primarily due to lower PVC resin prices and
improved cost control.



                                      -6-
<PAGE>   7




Long-term debt increased $5.2 million in the first half due to seasonal working
capital requirements primarily attributable to an increase in accounts
receivable and a reduction of payables. The debt level is down by $1.4 million
from the same period in the prior year as the Company returned to profitability
and experienced better working capital turn over.

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.

OUTLOOK

The Company experienced better product mix in the second quarter of 1998 as it
returned to profitability. Construction spending, new home sales and retail
sales trends appear to be steady heading into the second half of 1998. The
Company continues to make progress at recovering business lost due to internal
operating performance difficulties in 1997 as well as 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 in the second half of 1998 compared to the similar period in
1997.

The Company expects a strong operating cash flow and lower debt levels in the
third quarter due to anticipated profitability and strong working capital
management. Increased capital spending is expected in the second half of 1998 to
support additional capacity requirements and improved manufacturing and
distribution efficiency. 

As previously announced, the Company is conducting an evaluation of the
strategic alternatives available to reduce its exposure to highly volatile raw
material pricing. This evaluation process is continuing. 

The foregoing outlook contains 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 polyvinylchloride 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 and (viii) recovering the
confidence of key customers, (ix) resolution of the Union Pacific rail logistics
problems, and (x) a reversal in the country's general pattern of economic
improvement affecting the markets for the Company's products.




                                      -7-
<PAGE>   8


PART II

ITEM 4 - SUBMISSION OF MATTERS TO A VOTE OF SECURITY HOLDERS


On April 24, 1998, the Company held its Annual Meeting of Shareholders. At the
meeting, 13,415,684 Common Shares (90.01% of the Common Shares outstanding) were
voted. An increase in the number of Common Shares covered by The Lamson &
Sessions Co. 1998 Incentive Equity Plan was approved by a vote of 11,596,319
shares For, 354,651 shares Against, and 124,615 shares Abstained. The following
directors were elected to Class I and received the votes indicated next to their
names:




                                                               WITHHELD
               CLASS I                    FOR                 AUTHORITY
     ----------------------           ----------              ----------
     James T. Bartlett                11,870,686               204,899
     Francis H. Beam, Jr.             11,870,986               204,599
     Martin J. Cleary                 11,871,296               204,289
     William H. Coquillette           11,870,878               204,707




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 July 4, 1998.




                                      -8-
<PAGE>   9


                                   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:________________             By /s/ JAMES J. ABEL
                                    --------------------------------------------
                                           Executive Vice President, Secretary,
                                           Treasurer and Chief Financial Officer



                                      -9-
<PAGE>   10


THE LAMSON & SESSIONS CO. AND SUBSIDIARIES

EXHIBIT (11) - COMPUTATION OF EARNINGS PER COMMON SHARE


The following table sets forth the computation of basic and diluted earnings per
share:


(Dollars and shares in thousands)


<TABLE>
<CAPTION>
                                                                          Second Quarter Ended                First Half Ended
                                                                     -----------------------------    ------------------------------
                                                                         1998            1997             1998              1997
                                                                     -----------      -----------     ---------------   ------------
 <S>                                                                   <C>              <C>              <C>               <C>    
Basic Earnings-Per-Share Computation
 Net Income                                                            $ 2,351          $ 1,975          $ 2,025           $ 4,132
                                                                       =======          =======          =======           =======

 Average Common Shares Outstanding                                      13,425           13,310           13,420            13,308
                                                                       =======          =======          =======           =======

Basic Earnings Per Share                                               $  0.18          $  0.15          $  0.15           $  0.31
                                                                       =======          =======          =======           =======


Diluted Earnings-Per-Share Computation
Net Income                                                             $ 2,351          $ 1,975          $ 2,025           $ 4,132
                                                                       =======          =======          =======           =======

Basic Shares Outstanding                                                13,425           13,310           13,420            13,308

Stock Options calculated under the Treasury Stock Method                   113              232              111               230
                                                                       -------          -------          -------           -------

Total Shares                                                            13,538           13,542           13,531            13,540
                                                                       =======          =======          =======           =======

Dilluted Earnings Per Share                                            $  0.17          $  0.15          $  0.15           $  0.31
                                                                       =======          =======          =======           =======
</TABLE>





                                      -10-
<PAGE>   11


                    FOR FURTHER INFORMATION, PLEASE CONTACT:

                                  JAMES J. ABEL
                      EXECUTIVE VICE PRESIDENT, SECRETARY,
                      TREASURER AND CHIEF FINANCIAL OFFICER
                            THE LAMSON & SESSIONS CO.
                                 (216) 766-6557









                                      -11-