Lee's caretaker reign lasted just 90 minutes and saw Town beaten 7-2 by Shrewsbury in a game that left chairman David Cardoza 'embarrassed and humiliated'.
He joins his former boss Gary Johnson in leaving the club with ex-England international Flowers, assisted by Andy Holt, taking the reins for now.
"Before Saturday, I was going towards an up-and-coming manager," Cardoza told BBC Radio Northampton.
"But now I think we may need a little bit of experience."
Flowers has managerial experience with Stafford Rangers and was also assistant to Iain Dowie at Coventry, QPR and Hull. Dowie, currently out of work, is a 25/1 chance to become the next permanent manager at Sixfields.