<PAGE>

                                                                    EXHIBIT 31.2
                            THE LUBRIZOL CORPORATION
                          Rule 13a-14(a) Certification

I, Charles P. Cooley, certify that:

1. I have reviewed this annual report on Form 10-K of The Lubrizol Corporation;

2. Based on my knowledge, this report does not contain any untrue statement of a
material fact or omit to state a material fact necessary to make the statements
made, in light of the circumstances under which such statements were made, not
misleading with respect to the period covered by this report;

3. Based on my knowledge, the consolidated financial statements, and other
financial information included in this report, fairly present in all material
respects the financial condition, results of operations and cash flows of the
registrant as of, and for, the periods presented in this report;

4. The registrant's other certifying officer and I are responsible for
establishing and maintaining disclosure controls and procedures (as defined in
Exchange Act Rules 13a-15(e) and 15d-15(e)) and internal control over financial
reporting (as defined in Exchange Act Rules 13a-15(f) and 15d-15(f)) for the
registrant and we have:

      (a)   designed such disclosure controls and procedures, or caused such
            disclosure controls and procedures to be designed under our
            supervision, to ensure that material information relating to the
            registrant, including its consolidated subsidiaries, is made known
            to us by others within those entities, particularly during the
            period in which this report is being prepared;

      (b)   designed such internal control over financial reporting, or caused
            such internal control over financial reporting to be designed under
            our supervision, to provide assurance regarding the reliability of
            financial reporting and the preparation of financial statements for
            external purposes in accordance with generally accepted accounting
            principles;

      (c)   evaluated the effectiveness of the registrant's disclosure controls
            and procedures and presented in this report our conclusions about
            the effectiveness of the disclosure controls and procedures, as of
            the end of the period covered by this report based upon such
            evaluation; and

      (d)   disclosed in this report any change in registrant's internal control
            over financial reporting that occurred during registrant's most
            recent fiscal quarter that has materially affected, or is reasonably
            likely to materially affect, the registrant's internal control over
            financial reporting; and

5. The registrant's other certifying officer and I have disclosed, based on our
most recent evaluation of internal control over financial reporting, to the
registrant's auditors and the audit committee of the registrant's board of
directors (or persons performing the equivalent functions):

      (a)   all significant deficiencies and material weaknesses in the design
            or operation of internal control over financial reporting which are
            reasonably likely to adversely affect the registrant's ability to
            record, process, summarize and report financial information; and

      (b)   any fraud, whether or not material, that involves management or
            other employees who have a significant role in the registrant's
            internal control over financial reporting.

/s/ Charles P. Cooley
-----------------------
Charles P. Cooley
Chief Financial Officer
March 2, 2005