<PAGE>

                                                                    EXHIBIT 31.1

                                  CERTIFICATION

    I, Crit S. DeMent, certify that:

1.  I have reviewed this annual report on Form 10-K for the fiscal year ended
    December 31, 2004 of Lease Equity Appreciation Fund I, L.P.;

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 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(s) 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 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 reasonable 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 on such evaluation; and

    (d) Disclosed in this report any change in the registrant's internal control
        over financial reporting that occurred during the registrant's most
        recent fiscal quarter (the registrant's fourth fiscal quarter in the
        case of an annual report) 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(s) 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.

Date: March 31, 2005                         /s/ Crit S. DeMent
                                             -----------------------------------
                                             Name: Crit S. DeMent
                                             Title: Chief Executive Officer