When aai industry is active and using the "Add lumber item" and "Assembling machines cost wood" settings, lumber should probably be added to the burner assembling machine rather than the assembling machine 1.
Also with aai industry, with the use of "Inserters cost wood". Lumber should be added to the burner inserter recipe and removed from inserter and long handed inserter recipes, as aai industry changes recipes such that inserters require the previous inserter.
Also, I think the lumber recipe is too quick, it can consume an entire stack of wood in a very short amount of time. I would prefer to see the animation run longer. :)
When I say "should", that is just my opinion of course, do as you think best. :)