Mr Lewis was asked to investigate after remarks made by Graham Stringer, Labour MP for Manchester Blackley, during a House of Commons debate. Mr Stringer made his speech after Mancat's principal, Peter Tavernor, had been annoyed by the conduct of LSC auditors last autumn.
Following the audit, the LSC clawed back pound;300,000 of additional learning support (ALS) money which it said the college had wrongly claimed.
Mr Stringer told FE Focus there had been resentment among senior management that auditors concentrated on lists of students from ethnic minorities.
Mr Stringer spoke of management's belief that the audit was "carried out in a racist way". "That is not to say any individual member of the LSC is racist; the process is at fault," he said. "If we are dealing with young people - and 50 per cent are from ethnic minorities - there will be difficulties."
He added that auditors should be more responsive to students who could not write English and praised what he described as Mancat's "innovative working arrangements".
But Ivan Lewis told FE Focus: "I asked officials to look into concerns raised by Mr Stringer, and to identify what was being done, to ensure that institutional racism does not exist within the LSC's funding and audit arrangements.
"I subsequently wrote to Mr Stringer explaining that I do not believe the LSC's arrangements to be institutionally racist.
"I also explained that the LSC was embarking on an independent review of the way its provision of post-16 learning affects the promotion of equality and diversity.
"Given that the first phase is looking at funding arrangements for ALS and English for speakers of other languages, which were at the heart of the Mancat dispute, I see no benefit in commissioning further investigative work."
Liz Davis, executive director of Manchester LSC, has always denied the allegations. "I have nothing to add to the response of Ivan Lewis," she said.