#1
I've seen a lot of Erik Mongrain and Preston Reed stuff on youtube.

I was just wondering what kind of things should I know before composing lap tapping pieces?
#2
Actually I've never heard about Lap Tapping, but it sound very cool to me.

I think it's important to know where the notes on the fretboards are, that you want to play. Familiarize yourself with open tunings and look for some nice-sounding chords, that are possible to tap in the open tuning you want to compose.

Your guitar should have the lowerst action that is possible, and you should practice where to hit the notes, like when hammering on. Satriani said that it's much easier to practise where to hammer on, than building up strength.