Depending on how well the lath nails hold, you may be able to pull the lath off by hand after pulling off one initial nail. After a bit of experimentation, you should be able to find the easiest way to deal with your lath. Wall with surface removed. Now that the wall surfaces have been removed, you're left with the framing, which may have wiring and plumbing running through it. At this point you can pull the deactivated wiring out of the back of the electrical boxes, pull it through any holes in the framing, and coil it up out of the way.
Plumbing is another matter.
The water needs to be shut off, and the pipes cut and plugged, or perhaps rerouted if necessary. If this is above your abilities as a plumber, bring in a professional. With wiring and plumbing out of the way, the framing is ready to be removed. Then take each half and, by working it back and forth, pull it off of the nails that hold it to the top or bottom plate. After all of the free studs are removed, the end studs are next.