After clinching a deal with a Chinese battery maker in 2016, James Brown figured bankers would be eager to fund his new lithium mine. Altura Mining Ltd. was racing to ship the raw material from Australia to the world’s biggest electric vehicle market as demand was surging. Instead, while lithium prices kept rising, Brown spent a Christmas holiday cold-calling lenders and jetted around the globe to raise the money. Eventually, Minneapolis-based Castlelake LP, a private equity firm, helped arrange $110 million in bonds.