<PAGE>   1
                                  UNITED STATES
                       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 March 31, 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 0-4065-1

                          LANCASTER COLONY CORPORATION
             (Exact name of registrant as specified in its charter)


            OHIO                                        13-1955943
(State or other jurisdiction of             (I.R.S. Employer Identification No.)
incorporation or organization)


                   37 WEST BROAD STREET, COLUMBUS, OHIO 43215
                    (Address of principal executive offices)
                                   (Zip Code)

                                  614-224-7141
              (Registrant's telephone number, including area code)

                                      NONE
              (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, and (2) has been subject to such filing
requirements for the past 90 days. Yes X  No
                                      ---   ---

       As of March 31, 1998, there were approximately 43,194,000 shares of
common stock, no par value per share, outstanding.

                                     1 of 10

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                  LANCASTER COLONY CORPORATION AND SUBSIDIARIES

                                      INDEX


                                                                   Page No.
                                                                   --------
Part I.  Financial Information

    Condensed Consolidated Balance Sheets -
       March 31, 1998 and June 30, 1997                               3

    Condensed Consolidated Statements of Income -
       Three Months and Nine Months
       Ended March 31, 1998 and 1997                                  4

    Condensed Consolidated Statements of Cash Flows -
       Nine Months Ended March 31, 1998 and 1997                      5

    Notes to Condensed Consolidated Financial Statements              6

    Management's Discussion and Analysis of the Results
       of Operations and Financial Condition                          7-8

Part II.  Other Information

    Item 6 - Exhibits and Reports on Form 8-K                         9

    Signatures                                                        9

    Exhibit 27 - Financial Data Schedule                              10

                                     2 of 10

<PAGE>   3
                  LANCASTER COLONY CORPORATION AND SUBSIDIARIES

                      CONDENSED CONSOLIDATED BALANCE SHEETS

<TABLE>
<CAPTION>
                                                                                     March 31         June 30
                                                                                      1998             1997
                                                                                   -----------      ------------
                                                                                   (Unaudited)
<S>                                                                                <C>              <C>         
ASSETS
  Current Assets:
       Cash and equivalents                                                        $ 24,951,000     $ 32,109,000

       Receivables - net of allowance for doubtful accounts                         121,906,000      102,457,000

       Inventories:
          Raw materials and supplies                                                 47,381,000       42,339,000
          Finished goods and work in process                                        106,326,000      118,912,000
                                                                                   ------------     ------------
            Total inventories                                                       153,707,000      161,251,000

       Prepaid expenses and other current assets                                     16,611,000       12,966,000
                                                                                   ------------     ------------

            Total current assets                                                    317,175,000      308,783,000

  Property, Plant and Equipment - At cost                                           368,304,000      337,301,000
  Less Accumulated Depreciation                                                     202,061,000      185,992,000
                                                                                   ------------     ------------
            Property, plant and equipment - net                                     166,243,000      151,309,000

  Goodwill - net of accumulated amortization                                         37,191,000       19,810,000

  Other Assets                                                                        9,461,000        4,492,000
                                                                                   ------------     ------------

  Total Assets                                                                     $530,070,000     $484,394,000
                                                                                   ============     ============


LIABILITIES AND SHAREHOLDERS' EQUITY

  Current Liabilities:
       Current portion of long-term debt                                           $    550,000     $    545,000
       Accounts payable                                                              44,726,000       33,203,000
       Accrued liabilities                                                           32,280,000       39,956,000
                                                                                   ------------     ------------

            Total current liabilities                                                77,556,000       73,704,000

  Long-Term Debt - Less current portion                                              30,275,000       30,685,000

  Other Noncurrent Liabilities                                                        7,768,000        7,895,000

  Deferred Income Taxes                                                               3,777,000        4,110,000

  Shareholders' Equity:
       Preferred stock - authorized 3,050,000 shares
          issuable in series; Class A - $1.00 par value,
          authorized 750,000 shares; Class B and C -
          no par value, authorized 1,150,000 shares each;
          outstanding - none
       Common stock - authorized 75,000,000 shares;
          issued March 31, 1998 - no par value -
          47,072,000 shares; June 30, 1997 -
          no par value - 31,247,000 shares                                           49,824,000       43,573,000

       Retained earnings                                                            460,089,000      404,783,000

       Foreign currency translation adjustment                                           89,000           75,000
                                                                                   ------------     ------------

            Total                                                                   510,002,000      448,431,000

       Less:
          Common stock in treasury, at cost
            March 31, 1998 - 3,878,000 shares;
            June 30, 1997 -  2,230,000 shares                                        99,308,000       80,431,000
                                                                                   ------------     ------------

            Total shareholders' equity                                              410,694,000      368,000,000
                                                                                   ------------     ------------

  Total Liabilities and Shareholders' Equity                                       $530,070,000     $484,394,000
                                                                                   ============     ============
</TABLE>

  See Notes to Condensed Consolidated Financial Statements

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                  LANCASTER COLONY CORPORATION AND SUBSIDIARIES

                   CONDENSED CONSOLIDATED STATEMENTS OF INCOME

                                   (UNAUDITED)

<TABLE>
<CAPTION>
                                       Three Months Ended                  Nine Months Ended
                                            March 31                            March 31
                                     1998              1997              1998              1997
                                 ------------      ------------      ------------      ------------
<S>                              <C>               <C>               <C>               <C>          
Net Sales                        $237,628,000      $218,141,000      $775,556,000      $696,082,000

Cost of Sales                     161,378,000       148,984,000       529,106,000       478,290,000
                                 ------------      ------------      ------------      ------------

Gross Margin                       76,250,000        69,157,000       246,450,000       217,792,000

Selling, General and
  Administrative Expenses          39,964,000        34,499,000       127,582,000       111,403,000
                                 ------------      ------------      ------------      ------------

Operating Income                   36,286,000        34,658,000       118,868,000       106,389,000

Other Income (Expense):
      Interest expense               (637,000)         (633,000)       (1,995,000)       (1,941,000)
      Interest income and
        other - net                   868,000           (11,000)          663,000            30,000
                                 ------------      ------------      ------------      ------------

Income Before Income Taxes         36,517,000        34,014,000       117,536,000       104,478,000

Taxes Based on Income              13,721,000        12,992,000        44,912,000        39,791,000
                                 ------------      ------------      ------------      ------------

Net Income                       $ 22,796,000      $ 21,022,000      $ 72,624,000      $ 64,687,000
                                 ============      ============      ============      ============

Net Income Per Common
  Share:
      Basic                             $ .53             $ .48             $1.68             $1.46
      Diluted                           $ .53             $ .48             $1.67             $1.46

Cash Dividends Per Common
  Share                                 $ .140            $ .120            $ .400            $ .353

Weighted Average Common
  Shares Outstanding:
      Basic                        43,183,000        44,111,000        43,351,000        44,180,000
      Diluted                      43,297,000        44,156,000        43,445,000        44,231,000
</TABLE>


See Notes to Condensed Consolidated Financial Statements

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                  LANCASTER COLONY CORPORATION AND SUBSIDIARIES

                 CONDENSED CONSOLIDATED STATEMENTS OF CASH FLOWS

                                   (UNAUDITED)

<TABLE>
<CAPTION>
                                                                Nine Months Ended
                                                                     March 31
                                                             1998              1997
                                                          -----------      ------------
<S>                                                       <C>               <C>         
CASH FLOWS FROM OPERATING ACTIVITIES:
  Net income                                              $72,624,000       $64,687,000
  Adjustments to reconcile net income to net
     cash provided by operating activities:
     Depreciation and amortization                         24,351,000        20,427,000
     Deferred income taxes and other noncash charges       (2,360,000)         (768,000)
     Loss (gain) on sale of property                         (747,000)          232,000
     Changes in operating assets and liabilities:
        Receivables                                       (17,684,000)       (2,416,000)
        Inventories                                         8,855,000        (8,032,000)
        Prepaid expenses and other current assets          (1,673,000)       (2,679,000)
        Accounts payable                                   10,179,000         5,190,000
        Accrued liabilities                                (8,556,000)        1,240,000
                                                          -----------       -----------

     Net cash provided by operating activities             84,989,000        77,881,000
                                                          -----------       -----------

CASH FLOWS FROM INVESTING ACTIVITIES:
  Cash paid for acquisition, net of cash acquired         (19,749,000)
  Payments on property additions                          (32,919,000)      (28,552,000)
  Proceeds from sale of property                            2,016,000            38,000
  Other - net                                              (7,637,000)       (3,091,000)
                                                          -----------       -----------

     Net cash used in investing activities                (58,289,000)      (31,605,000)
                                                          -----------       -----------

CASH FLOWS FROM FINANCING ACTIVITIES:
  Purchase of treasury stock                              (18,877,000)      (16,794,000)
  Payment of dividends                                    (17,318,000)      (15,599,000)
  Payments on long-term debt, including
    payment of acquisition debt                            (3,928,000)         (610,000)
  Common stock issued upon exercise of stock
    options and related tax benefits                        6,251,000         5,048,000
                                                          -----------       -----------

     Net cash used in financing activities                (33,872,000)      (27,955,000)
                                                          -----------       -----------

Effect of exchange rate changes on cash                        14,000            28,000
                                                          -----------       -----------
Net change in cash and equivalents                         (7,158,000)       18,349,000
Cash and equivalents at beginning of year                  32,109,000         4,670,000
                                                          -----------       -----------
Cash and equivalents at end of period                     $24,951,000       $23,019,000
                                                          ===========       ===========


SUPPLEMENTAL DISCLOSURE OF OPERATING CASH FLOWS:

    Cash paid during the period for:
        Interest                                          $ 2,543,000       $ 2,537,000
                                                          ===========       ===========
        Income taxes                                      $52,084,000       $44,376,000
                                                          ===========       ===========
</TABLE>

See Notes to Condensed Consolidated Financial Statements

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                  LANCASTER COLONY CORPORATION AND SUBSIDIARIES
              NOTES TO CONDENSED CONSOLIDATED FINANCIAL STATEMENTS
                  FOR THE PERIODS ENDED MARCH 31, 1998 AND 1997

(1)       The interim condensed consolidated financial statements are unaudited
          but, in the opinion of management, reflect all adjustments necessary
          for a fair presentation of the results of operations and financial
          position for such periods.  All such adjustments reflected in the
          interim condensed consolidated financial statements are considered to
          be of a normal recurring nature.  The results of operations for any
          interim period are not necessarily indicative of results for the full
          year.  Accordingly, these financial statements should be read in
          conjunction with the financial statements and notes thereto contained
          in the Company's annual report on Form 10-K for the year ended June
          30, 1997.

(2)       On January 27, 1998, a three-for-two stock split was effected whereby
          one additional common share was issued for each two shares outstanding
          to shareholders of record on January 6, 1998. Accordingly, all per
          share data and the weighted average common shares outstanding for the
          period ended March 31, 1997 in the accompanying condensed consolidated
          financial statements have been retroactively adjusted for this split.

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                  LANCASTER COLONY CORPORATION AND SUBSIDIARIES
                   MANAGEMENT'S DISCUSSION AND ANALYSIS OF THE
                  RESULTS OF OPERATIONS AND FINANCIAL CONDITION
                  FOR THE PERIODS ENDED MARCH 31, 1998 AND 1997

                              RESULTS OF OPERATIONS

       Consolidated net sales of $775,556,000 and $237,628,000 for the
respective nine month and three month periods ended March 31, 1998 increased 11%
and 9% over the corresponding 1997 totals of $696,082,000 and $218,141,000.
Sales of the Glassware and Candles segment increased during both periods
primarily as a result of the growth in the sales of candles and related
products. The sales of the Specialty Foods segment also benefited during these
periods from the July 1997 acquisition of the Chatham Village crouton business,
greater foodservice opportunities and the success of certain frozen product
lines, particularly Texas Garlic Toast. Automotive sales were up modestly for
the nine months and slightly declined during the most recent quarter. Improved
demand from original equipment manufacturers for floormats and aluminum truck
accessories was offset by weaker aftermarket demand as influenced by competitive
conditions affecting the bedliner industry.

       Increased gross margins within the Specialty Foods segment contributed to
the higher consolidated gross margin percentages of 31.8% and 32.1% reported for
the respective nine month and three month periods ended March 31, 1998 compared
to 31.3% and 31.7% achieved in the corresponding periods ended March 31, 1997.
The Specialty Foods segment benefited from such factors as production
efficiencies, improvement in frozen food margins and lower raw material costs.
On the basis of current market conditions, however, these material costs are
expected to compare less favorably to fiscal 1997 costs over the remainder of
fiscal 1998.

       Within the Glassware and Candles segment, fiscal 1998 gross margin
percentages declined. Among the factors contributing to the nine month decline
was unabsorbed overhead associated with a major rebuild of a glass melting tank
and generally lower glassware production levels. Increased raw material costs
and a less favorable sales mix also contributed to a decline in the margins
associated with the sales of candles. Automotive segment margins were adversely
affected by the competitive conditions affecting aftermarket bedliner sales.

       Consolidated selling, general and administrative expenses totaled
$127,582,000 and $39,964,000 for the respective nine and three month periods
ended March 31, 1998 which reflected an increase of 15% and 16% over the
corresponding 1997 totals of $111,403,000 and $34,499,000. This growth was
primarily attributable to increased consolidated sales volumes and increased
promotional activities within the Specialty Foods Segment and includes certain
costs associated with the acquisition of new customers or markets.

       The increase in interest and other income for the nine and three months
ended March 31, 1998 compared to the corresponding periods of fiscal 1997 is
attributable to gains on the sales of property, plant and equipment recognized
during the third quarter of fiscal 1998.

       Overall, consolidated operating income increased to $118,868,000 and
$36,286,000, a 12% and 5% increase over the $106,389,000 and $34,658,000
realized for the respective nine and three month periods ended March 31, 1997.
Consolidated net income also increased to $72,624,000 and $22,796,000 for the
nine and three month periods ending March 31, 1998, resulting in a 12% and 8%
increase from the prior year's corresponding nine and three month period totals
of $64,687,000 and $21,022,000.

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<PAGE>   8
                              FINANCIAL CONDITION

       Net working capital at March 31, 1998 totaled $239,619,000 compared to
$235,079,000 as of the preceding June 30. The Company's working capital ratio
decreased slightly from 4.2:1.0 at June 30 to 4.1:1.0 at March 31. Consolidated
accounts receivable increased $19,449,000 or 19%, as influenced by the relative
strength of shipments in the last month of the most recent period.

       With respect to cash flows, net cash provided by operating activities for
the nine months ended March 31, 1998 totaled $84,989,000 compared to $77,881,000
for the corresponding periods of 1997. The increase in net income contributed to
this increase.

       Notable investing activities for the nine months ended March 31, 1998
included $32,919,000 paid for property additions and $19,749,000 paid to acquire
the Chatham Village crouton business in July. These amounts were financed
through the use of internally generated funds.

       Significant financing activities of the Company during the first nine
months of fiscal 1998 included $18,877,000 paid to purchase treasury stock and
$17,318,000 paid in dividends. The latter amount compared to $15,599,000 paid
during the comparable period of 1997. The increase in dividends paid reflects an
increase in the stated dividend rate from $.353 paid through March, 1997 to $.40
paid through March, 1998 as adjusted for the 3 for 2 stock split which occurred
on January 27, 1998. Management anticipates that cash provided from operations
and from the currently available discretionary bank credit lines will be
adequate to meet the Company's foreseeable cash requirements over the remainder
of fiscal 1998.

       The Company is currently in the process of modifying or replacing certain
information systems in order to address potential processing deficiencies
regarding the year 2000. In accordance with current accounting guidance, all
modification costs for the year 2000 will be charged to expense as incurred
while replacement costs will be capitalized and amortized over the asset's
useful life.

       It is not presently believed that these changes to information systems
will have an adverse impact on operations or that the expenditures related
thereto will be material to the Company's financial position or results of
operation in any given year. However, due to the nature of this issue, it is
possible that a failure by the Company, its customers or its suppliers to make a
complete and timely assessment of the necessary requirements could have a
material adverse affect on the Company's business, results of operations and/or
financial position.

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<PAGE>   9

                           PART II. OTHER INFORMATION

Item 6 - Exhibits and Reports on Form 8-K

      (a)     Exhibit 27 - Financial Data Schedule

      (b)     Reports of Form 8-K - There were no reports filed on Form 8-K for
              the three months ended March 31, 1998.

                                   SIGNATURES

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

                                        LANCASTER COLONY CORPORATION

Date:   May 8, 1998                     BY: /s/ John B. Gerlach, Jr.
      --------------                       ------------------------------
                                           JOHN B. GERLACH, JR.
                                           Chairman, Chief Executive
                                           Officer and President


Date:   May 8, 1998                     BY: /s/ John L. Boylan
      --------------                       ------------------------------
                                           JOHN L. BOYLAN
                                           Treasurer, Vice President,
                                           Assistant Secretary and 
                                           Chief Financial Officer
                                           (Principal Financial and
                                           Accounting Officer)

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