I removed two room's worth of walls and ceiling horsehair plaster and wood lath from a home built in 1890. Would the plaster or paint used in those days cause the wood to release any toxins when burned? I'm wondering if the material can safely be used for firewood.
There might also be asbestos in the plaster and contaminating the lath.
Did you have the wall tested prior to demolition? (I'm guessing no) You may have to be very careful with this material and possibly apply a complex and detailed cleaning of the site to render it safe, sorry to say.
Here's to hoping that it doesn't have asbestos... In USA the use of asbestos in plaster walls is uncommon prior to 1920, however the wall may have been re-plastered after the house was built.
If you do decide to burn it and it has asbestos or lead in it you may be violating health or pollution laws in your area, but at least make sure that everyone is a long ways away from the fire. (It may be better, eg. safer and more law-abiding, just to hire the appropriate disposal experts and have them clean the site and dispose of the waste)
Wood smoke itself contains many toxins and carcinogens. I mention it because folks have the false impression that it's somehow more "natural" than other types of smoke, and therefore safer.
If you're managing your fire well, the little bit of extra stuff that clings to the lath shouldn't be an issue. (How would there be a substantial amount of paint on it?)
That old lathe board makes great kindling wood to start a fire. It gets very hot, so I wouldn't load the stove to the top with it. Your whole wood stove is full of toxins when lit so it's all going out the chimney anyways.
I'd definitely be concerned about lead based paint - land fill is probably the safest bet. You could test the paint for lead.