Can you build data centers in a desert without draining the water supply? Utah is finding out.

In late September, Governor Spencer Cox of Utah stood on the shores of the drying Great Salt Lake, flanked by top legislative leaders and wealthy developers as he unveiled a new partnership between the state government, a nonprofit, and business owners, that he said could help refill Utah’s iconic inland sea in time for the 2034 Winter Olympics.

The lake needs to rise by more than 6 feet to reach what scientists and state resource managers consider a minimum healthy elevation, a goal...