I've encountered this problem in Linuxmint LXDE and Lubuntu. I don't know if it's a shortcoming of LXDE or is limited to the distros I've tried so far, so I thought I'd ask here.
I'm a leftie. When I set the mouse to be left-handed on my laptop, I lose tap-to-click because tapping my touchpad works like a right-click for right-handed people or a left-click for left-handed people. For a left-handed person, tapping the touch pad should act like a right-click, which would be a left-click for right-handed people.
So has LXDE not figured this out yet or did I just pick a couple of broken distros for trying out LXDE? Micro$oft figured this out long, long ago and other desktops in several other GNU/Linux distros get it right.