In 2009 (and mayne also 2010) Flybe operated a Leeds-Gatwick route. I don't have yield figures but the fact that the route is no more suggests it was not hugely profitable.
Leeds to London by train takes about the same amount of time as Liverpool-London anx has a similiar frequency. Further I imagine that there is more commerce and money floating around Leeds compared to Liverpool
If Leeds can't keep a London route what chance is there for Liverpool given its location near Manchester airport ?