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I still wood like to wood plank an accent wall in my dining room

Not sure how thin the wood should be and what would be the best dimensions for this project
I would be sure to attach the reclaimed wood to the studs, but It may not be necessary to remove the lathe. The wood will get heavy quick and you want it attached to studs.
Here's a good video on finding the studs in plaster walls for attaching the wood: https://www.youtube.com/watch?v=JOLRl8aqWFw
This answer should help: https://www.stretcher.com/stories/03/03jul28h.cfm
Do not remove the plaster. Glue and nail the reclaimed wood over the plaster walls. Per buildindg and insurance codes you need a fire barrier on the walls. That is what the plaster is for. If you remove the plaster you will need to put up 1/2" drywall to replace it. Then the wood over that.
Hi Justin: Like William said (Hi William), I'd leave the plaster and put your new wood over the plaster. Be sure you nail into the studs. Not knowing if the studs are the correct distance apart, before you start see if you can find the studs so you know where they are. You can either write the distances down or tape some paper to the floor and make a mark where the studs are on that. Also, near the floor, poke a small nail into the wall on either side of the stud to see how wide it is. If it's a really old house, one never knows :) You will want to nail into the middle of the stud. Good luck.