Is it safe to use old wood lath from demolition as 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)