Drywall over lath and plaster?

If the plaster wall is straigh,( cross your fingers) it should not be a problem. if not, removing plaster and lathe will be a very messy job, especially if you are living in the house.

remove woodwork first then when reinstalling woodwork use strips of wood to even it out.

I'd tend to agree with Sensible here, lath and plaster walls are notorious for being extremely wavy, especially around the windows and doorways. Frequently, the plaster comes right out to be flush with the outer edges of the doors and windows and what's he going to do there. When he installs drywall at that point the drywall is going to stick out farther than the woodwork, necessitating that he install new woodwork over the old woodwork. Besides, by tearing off the old plaster and lathe, you'll be able to see where the wiring and plumbing run, which can come in very handy at later times. It could also keep you or him, from driving a nail or screw into a live wire or charged water pipe. Either of those scenarios aren't pretty.

First, the drywall will not go over the plaster evenly. He would need extra long nails also. When he hammers the nails in, or even using screws, he will be damaging the plaster. He will regret doing this.

The walls will be fine, this is done all the time. He will have to use longer screws to fasten it. Screw into the studs, not the lath. Yes you are adding more weight, but it is dispersed over the area, not concentrated on one spot.