without plaster you dont *need* the lath and would have a hard time getting rid of the plaster bits for a smooth install of the beadboard. be prepared for some wacky studs, and some shims might be needed here and there but maybe not.

I'd go down to the bear studs, clean things up and then add your beadboard or whatever you want.

My girlfriend wire brushed her lath and put a coat of clear poly on it and trimmed it out with a cream or putty color trim and it looks awesome!! Very old colonial house.

You'd have to see what worked the best. If you have a pry bar and can pry the lathe off the stud easily, go for it. One way or the other you're going to be pulling nails or pounding them in depending on which is easier. Try youtube for videos on how to remove it.

Please ware a respirator, and ventilate the room while working.

The dust may contain Lead or asbestos particles.

And yes I would take it down to the studs.