As FE Focus reported last week, colleges have been warned against doing business with the private training company, which specialises in book-keeping and information technology courses.
The LSC is concerned about the company's practice of recommending students to its own in-house loan company for finance to pay for their course fees.
Robert Webb, a director of The Learning Library until April last year, got an 18-month prison sentence in 1999 for cheating the Inland Revenue.
If Mr Haysom needs to learn more about the company, he could call up his former colleagues at the Daily Mirror, for which he was responsible during his previous job as a director of Trinity Mirror.
The newspaper quoted Steven Wines, The Learning Library's managing director, twice last year, in stories promoting distance-learning.
In one, on June 11, he said: "There are a lot of distance-learning companies around so you should look for one with an established track record."