The European country holds between 1.2 to 1.4 million tonnes of lithium, located mostly around the tiny village of Cinovec, on the border with Germany.
The firm, the world's largest primary silver producer and Mexico's second-largest gold miner, said output of the grey precious metal hit 13.5 million ounces in the quarter.
The miner said decision was unrelated to Elliott Management's call earlier this month to unlock shareholder value by spinning off about $22 billion of BHP's US oil assets.
BMI Research expects prices to continue sliding for at least the next five years on rising supplies from Australia and Brazil and expectations for a surplus.
Both iron ore and diamond output rose in the first quarter thanks to a continued ramping-up of the company's Minas Rio mine in Brazil and improvements in the gem market.