Is what you have actual reclaimed lath out the walls of an old plaster and lath house* ?? Or is this lath recently purchased from a lumber yard/hardware store ??
If you are going to do what you stated, then go to a lumber yard (hell, even Homeless Despot might have some) and buy some "thin wood" in Walnut, Beech, Oak, Maple, and Cherry. (Maybe even a flooring store would have what you are looking for), then you get various natural colors, without having to deal with cheap, rough-hewn, fast-grow pine that's going to warp all to hell 30 seconds after you install it.
Either way, having Rev nuke Pinterest is the best idea I've heard in awhile. Or you could have an accidental bonfire while she's not home.
In which case, it probably should not be warping, as 1) it's old, and 2) the plaster would have pulled most/all of the moist out.