The lath might add a little rigidity to the walls and floor/ceiling framing, but it is insignificant. The proper installation and fastening of sheetrock will easily accomplish the same thing. I can tell you that the lath is not considered a structural element of the house.
In the majority of such remodeling projects (where you have old style plaster and lathing), the best approach to updating the walls is to: Remove the lathing and old plaster, Then, install re-usable lathing, or purchase new lathing, vertically over the existing studs.
When you install your sheetrock (often using 52" Wide sheetrock)....The added lathing strips brings the finished wall surfaces back out to match the existing window and door casings widths (unless all of those are being replaced).
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