Exhibit 31.1

CERTIFICATION

I, Michael S. Leto,
certify that:



| | 1. | I have reviewed this annual report on Form 10-K, and all reports on Form 8-K containing distribution or servicing reports filed in respect of periods included in the year covered by this annual report, of Lehman ABS
Corporation, on behalf of Corporate Backed Trust Certificates, Goldman Sachs Capital I Securities-Backed Series 2004-7 Trust (the Trust);
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| | 2. | Based on my knowledge, and the annual compliance review required under the pooling or servicing, or similar, agreement, the information in these reports, taken as a whole, 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 as of the last day of the period covered by this annual report;
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| | 3. | Based on my knowledge, and the annual compliance review required under the pooling and servicing, or similar, agreement, the distribution or servicing information required to be provided to the Depositor by the Trustee
under the pooling and servicing, or similar, agreement, for inclusion in these reports is included in these reports;
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| | 4. | I am responsible for reviewing the activities performed by the Depositor and the Trustee under the pooling and servicing, or similar, agreement and based upon my knowledge and the annual compliance review required under
that agreement, and except as disclosed in the reports, the Depositor and Trustee have each fulfilled its obligations under that agreement; and
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| | 5. | The reports disclose all significant deficiencies, of which there were none, relating to the compliance by the Trustee and the Depositor with the minimum servicing or similar standards based upon the report provided by
an independent public accountant, after conducting a review in compliance with the Uniform Single Attestation Program for Mortgage Bankers or similar procedure, as set forth in the pooling and servicing, or similar, agreement that is included in
these reports.
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In giving the certifications above, I have reasonably relied on information provided to me by the following unaffiliated
party: U.S. Bank Trust National Association, as Trustee.



|                     |  |        |  |                                                     
|-------------------- |  | ------ |  | ----------------------------------------------------
|Date: March 30, 2015
|                     |  |       
|By:                  |  |        |  | /s/ Michael S. Leto                                 
|                     |  | Name:  |  | Michael S. Leto                                     
|                     |  | Title: |  | Executive Vice President and Chief Financial
Officer