I sprayed the front disc and caliper with half a can of brake cleaner
and this green stuff came off.

1. Any idea what the green stuff might be?
2. Do I always need to lube the slider after using brake cleaner on
front disc and caliper?

Thanks to everyone for the support and wonderful tips.

 

What was this green stuff? Where did it come from? (Exactly where?
Telling me from the caliper won't help me much. As it stands, all I know
about this stuff that came off is that it was green.)

You should always lube the caliper slider, especially if there's any
reason to doubt the effectiveness of the lube currently in place.