Yeah, there probably is a “drum clef”, although it might just be a convention, i.e., a system generally agreed upon, but with a number of variations.
Here is what DrumMagazine suggests:
When I was writing music with a friend in the 80s, we had come up with a similar system, where the kick notes were on the low f (bass clef), the snare was on the low a and the hi-hat on the high a - that left room for the cymbals above and the toms in between. It looked like this:
However, how Terry Bozzio notates his drums is anybody’s guess 
So, taken the simple system described above (and just notating the kick and the snare), I would transcribe M1 Lesson 2 like this:
Sorry about the hand-written notes - I hope it makes some sense!? Please note, the notation system is somewhat sloppy as I only write the essential rests, not, e.g., all the quarter rests that should also be there. So, it is implicitly understood that the snare notes are ALWAYS on 2 and 4 here. That should give you a “grid”.
In real life, I would talk to the drummer about what he intends to play. Mainly whether he/she intends to play the same pattern every time or whether he/she “improvises” the kick drum here. Also, for bar 8 (the fill), you just let him/her have that and don’t play along!
Hope this helps a bit!?