Can I drywall over plaster
You can drywall over the plaster, but you'll have to do the entire wall and screw through the plaster into the lath/studs.

Alternatively, you can fix the plaster itself.  The problem is, it's separated from the lath.  The fix for this is to drill shallow holes into the affected area JUST DEEP ENOUGH to penetrate the plaster, not the lath.  Drill the holes 4" apart in a grid pattern.

Then use a caulking gun and inject construction adhesive into each hole to create a glue layer behind the plaster between it and the lath.

Press the plaster up against the lath with a flat board, holding it ONLY UNTIL THE PLASTER STICKS.  Don't leave the board there too long or the glue will grab it too.  Slide the board up and down to keep it from sticking while the glue takes hold between the lath and plaster.

Allow it time to dry, then patch the holes and paint.