<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 April 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
                                                           -----
                 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)
<TABLE>
<CAPTION>

<S>                                              <C>
                    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)
</TABLE>

                                  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 April 4, 1998 the Registrant had outstanding 13,415,684 common shares.

                                      -1-

<PAGE>   2


PART I

ITEM 1 - FINANCIAL STATEMENTS

CONSOLIDATED STATEMENT OF OPERATIONS (UNAUDITED)

THE LAMSON & SESSIONS CO. AND SUBSIDIARIES

(IN THOUSANDS, EXCEPT PER SHARE DATA)
<TABLE>
<CAPTION>

                                                             FIRST QUARTER ENDED
                                                         -----------------------
                                                             1998           1997
                                                         --------       --------

<S>                                                      <C>            <C>
Net sales                                                $ 64,794       $ 68,844
Cost of products sold                                      52,536         53,951
                                                         --------       --------

GROSS PROFIT                                               12,258         14,893
Selling, general and
administrative expenses                                    11,447         12,629
                                                         --------       --------

OPERATING INCOME                                              811          2,264

Interest                                                    1,137            807
                                                         --------       --------
(LOSS) INCOME BEFORE INCOME TAXES                            (326)         1,457

Income tax benefit                                           --              700
                                                         --------       --------

NET (LOSS) INCOME                                        $   (326)      $  2,157
                                                         ========       ========

BASIC (LOSS) EARNINGS PER COMMON SHARE:                  $  (0.02)      $   0.16
                                                         ========       ========

DILUTED (LOSS) EARNINGS PER COMMON SHARE:                $  (0.02)      $   0.16
                                                         ========       ========

AVERAGE COMMON SHARES                                      13,416         13,546
                                                         ========       ========
</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>
                                                                     FIRST QUARTER                          FIRST QUARTER
                                                                          ENDED          YEAR END               ENDED
                                                                     ----------------------------------------------------
                                                                           1998            1997                  1997
                                                                     ----------------------------------------------------
<S>                                                                     <C>           <C>               <C>
 ASSETS
 CURRENT ASSETS
   Cash and cash equivalents                                            $     773     $      l,410      $        l,301
   Accounts receivable                                                     38,939           32,951              49,023
   Inventories
    Finished goods and work-in-process                                     40,721           39,532              44,989
    Raw materials and supplies                                              5,212            6,043               6,854
                                                                     ------------     ------------      --------------
                                                                           45,933           45,575              51,843
   Prepaid expenses and other                                              11,038           11,631               8,642
                                                                     ------------     ------------      --------------
 TOTAL CURRENT ASSETS                                                      96,683           91,567             110,809

 OTHER ASSETS                                                              14,959           14,598               9,846

 PROPERTY, PLANT AND EQUIPMENT                                            111,322          111,211             115,778
   Less allowances for depreciation and amortization                       56,777           54,882              54,690
                                                                     ------------     ------------      --------------
                                                                           54,545           56,329              61,088
                                                                     ------------     ------------      --------------
                                                 TOTAL ASSETS           $ 166,187     $    162,494      $      181,743
                                                                     ============     ============      ==============

 LIABILITIES AND SHAREHOLDERS' EQUITY
 CURRENT LIABILITIES
   Accounts payable                                                     $  24,189     $     27,734      $       26,972
   Accrued expenses and other liabilities                                  21,981           22,272              23,945
   Taxes                                                                    3,430            3,815               3,815
   Current maturities of long-term debt                                     3,795            3,759               3,626
                                                                     ------------     ------------      --------------
 TOTAL CURRENT LIABILITIES                                                 53,395           57,580              58,358

 LONG-TERM DEBT                                                            52,666           44,712              48,842

 POST-RETIREMENT BENEFITS AND OTHER LONG TERM LIABILITIES                  23,462           23,221              27,296

 SHAREHOLDERS' EQUITY
   Common shares                                                            1,342            1,341               1,331
   Other Capital                                                           73,417           73,409              72,815
   Retained earnings (deficit)                                            (37,005)         (36,679)            (24,869)
   Pension adjustment                                                      (1,090)          (1,090)             (2,030)
                                                                     ------------     ------------      --------------
                                                                           36,664           36,981              47,247
                                                                     ------------     ------------      --------------
 TOTAL LIABILITIES AND SHAREHOLDERS' EQUITY                             $ 166,187     $    162,494      $      181,743
                                                                     ============     ============      ==============
</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 QUARTER ENDED
                                                                                          1998                   1997
                                                                                      -------------          --------------

<S>                                                                                     <C>                    <C>
OPERATING ACTIVITIES
   Net (loss) income                                                                    $     (326)             $    2,157
   Adjustments to reconcile net income to cash used by operations:
      Depreciation and amortization                                                          2,682                   1,714
      Deferred income tax benefit                                                                -                    (725)
      Net change in working capital accounts:
        Accounts receivable                                                                 (5,988)                (12,397)
        Inventories                                                                           (358)                 (9,021)
        Prepaid expenses and other                                                             593                   2,460
        Current liabilities                                                                 (4,221)                  7,202
      Net change in other long-term items                                                     (214)                    176
                                                                                      -------------          --------------
CASH USED BY OPERATING ACTIVITIES                                                           (7,832)                 (8,434)

INVESTING ACTIVITIES
   Net purchases of property, plant and equipment                                             (804)                 (2,228)
                                                                                      -------------          --------------
CASH USED BY INVESTING ACTIVITIES                                                             (804)                 (2,228)

FINANCING ACTIVITIES
   Net change in secured credit agreement                                                    8,080                  11,307
   Net changes in long-term borrowing and capital lease obligations                            (90)                   (126)
    Exercise of stock options                                                                    9                      24
                                                                                      -------------          --------------
CASH PROVIDED BY FINANCING ACTIVITIES                                                        7,999                  11,205

(DECREASE) INCREASE IN CASH                                                                   (637)                    543
Cash at beginning of year                                                                    1,410                     758
                                                                                      -------------          --------------
CASH AT END OF THE PERIOD                                                               $      773             $     1,301
                                                                                      =============          ==============
</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) 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 PRONOUNCEMENTS

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 first quarter 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 first quarter of 1997 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 losses.

                                      -5-


<PAGE>   6


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

CONSOLIDATED STATEMENT OF OPERATIONS

Sales for the quarter were down 5.9% compared to the prior year quarter. This
decrease was driven by a 9% decline in the volume of rigid pipe products and by
the planned exit of some commodity sewer pipe products and wiring devices. It
also reflects a slight decrease in average PVC rigid pipe prices. These
decreases were partially offset by increases in sales of flexible pipe and
molded products sales.

Gross margin decreased by 12.5% to 18.9% in the first quarter of 1998 compared
to the first quarter of 1997. Plant utilization was slightly less than last
year's high first quarter rates. This reduced inventory levels and resulted in
less absorption of fixed manufacturing costs.

Selling, general and administrative expenses decreased 9.4% or $1.2 million in
the first quarter of 1998 compared to 1997. Lower commission expenses related to
lower sales levels coupled with controlled current period administrative costs,
allowed for these expenses to decrease slightly as a percentage of sales despite
the lower base of sales. In 1997, the Company incurred higher administrative
costs associated with the implementation of its business process and 
information technology project.

The increase in outstanding debt and borrowing rates generated the increase in
interest expense compared to the first quarter of 1997.


CONSOLIDATED BALANCE SHEET

Accounts receivable increased approximately $6.0 million compared to year-end
levels due to a higher concentration of sales later in the quarter period.
Accounts receivable decreased by $10.1 million from the prior year quarter
primarily due to stronger collection efforts and a modestly lower sales level.
Inventory remained constant compared to year-end levels, but was reduced by $5.9
million from the prior year quarter. Accounts payable decreased nearly $2.5
million compared to year-end levels. Total debt increased $8.0 million compared
to year-end as the secured credit line was used to fund working capital
requirements.

CONSOLIDATED STATEMENT OF CASH FLOWS

Cash used by operations was $7.8 million in 1998 compared to $8.4 million in the
prior year quarter. The cash use occurred primarily because of the seasonal
increase in accounts receivable during the quarter and the decrease in accounts
payable.

Investing activities used $1.4 million less in cash than the prior year quarter.
This reduction reflects the completion of the implementation of the business
process and information technology project during the first half of 1997.

                                      -6-


<PAGE>   7



OUTLOOK

Despite lower sales and profitability this quarter compared to the same quarter
in the prior year, the Company is in a better position to take advantage of
continued strength in its markets. The Company has reduced the substantial
operating losses experienced in the second half of 1997 through increased
customer satisfaction and delivery performance, better management of accounts
receivable and inventory, and increased capacity to support molded and priority
products. These factors combined with the Company's enhanced information
technology cause management to expect continued improvement in operating
results.

The Company's efforts are focused on regaining market share and increasing
customer satisfaction. The Company is encouraged by the continued strength in
estimated housing starts, new home sales, retail spending and consumer
confidence.

Working capital management has improved over the prior year and will also be a
focus of management for the remainder of 1998 as the Company utilizes the
capabilities provided by the new information technology to drive stronger
operating cash flow.

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.

These forward-looking comments are subject to the cautionary limitations in
connection with the `safe-harbor' provisions of the Private Securities
Litigation Reform Act of 1995 which are provided in the Company's report on Form
10-K filed in February 1998.

                                      -7-

<PAGE>   8


PART II

ITEM 1 - LEGAL PROCEEDINGS

The Company is a party to various claims and matters of litigation incidental to
the normal course of its business. Management believes that the final resolution
of these matters will not have a material adverse effect on the Company's
financial position.


ITEM 6 - EXHIBITS AND REPORTS ON FORM 8-K

        (a)     Exhibits.

                11  Compilation of Earnings Per 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 April 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
    ------------       ---------------------------------------------------------
                              James J. Abel
                        Executive Vice President, Secretary, Treasurer and
                        Chief Financial Officer


                                      -9-