Mine was cracked as well. Seems like a "pot metal" type of material. I would be cautious with applying heat to these considering the rarity.
Even TIG welding would be sketchy in my mind. I used JB Weld on the underside with decent results. But then again, my LV looks nothing like yours!
In doing some research into repairing pot metal I stumbled across Muggyweld products. The Muggyweld Super Alloy1 is a low temperature solder/weld material that can fix pot metal parts. Link to website with video: Muggyweld Products
Please note...I have not actually tried this product and would probably try to find some scrap pot metal part to practice on before attempting to repair a rare LV part.