In Tim Roughgarden's fantastic course on Algorithmic Game Theory, he begins the course by introducing basic mechanism design, and Myerson's Lemma. He then proves that Myerson's Lemma is valid for piecewise constant allocation functions. I would like to know if a proof also exists for piecewise linear allocation functions.
Milgrom's excellent Putting Auction Theory to Work is a reference for what you're looking for. If I'm not mistaken, Myerson's lemma works for quasi-linear payoffs.