I don't think there IS a "lesser of x AND y. " If you say x and y, that is the same as x + y. Just because one statement is written out in words and the other uses a mathematical shorthand, the meaning isn't changed. If you add two things, there will only be one answer. If you want to choose the lesser, you need a selection to choose from.
I'll offer a considered opinion, but not very forcefully. My feeling is that "X and Y" is correct.
My reasoning is as follows: You can say "the lesser of the two"; "the two" refers to a group (i.e. a single collective entity), so "the lesser of X and Y" is like saying "the lesser of the items in the group containing X and Y."
Thanks for the feedback. I have to admit that I'm pulled to X or Y. Mathematically, "or" fits, but when you look at the group concept (e.g. "lesser of the two") then "and" fits. Perhaps this is another grey area of the wonderfully, complex English language. Thanks again.