Research Burner assembler gives recipe only for copper Burner assembling machine, can't build this on Lignumis.

Which mod i need for Burner assembling machine (Gold-wood) ?

Can you send me a savegame either in Discord or post a download link here?

Can you send me a savegame either in Discord or post a download link here?

Sure
https://drive.google.com/file/d/10NRnGfNSzoq9PBxMczDE9wiR2dkDPulC/view?usp=sharing
https://drive.google.com/file/d/11OjckFkcIom0YMlhYHDqkSJaC-LTzpM4/view?usp=sharing

Lignumis, AAI Industry and Exotic Space Industries: Remembrance. That's a difficult combination. Exotic Space Industries seems to remove the Lignumian burner assembler without providing an alternative recipe. Since the compatibility is maintained on their side, I'd side report it there: https://mods.factorio.com/mod/exotic-space-industries-remembrance
Also incude the information about this combination of mods because it's important.