No, it was always like that. It's an Endorheic lake that formed 16,800 years ago and has been evaporating ever since. The water was not usable for anything when the Mormons arrived in 1847, which is why no meaningful settlements ever arose around the lake.

The loss of lake level isn't caused by climate change, though it is caused by people. The lake hit a record high as recently as 1987. But the problem is increasing diversion of the rivers that feed the lake as Utah develops. Utah's population has doubled since 1987, and it's one of the fastest growing states in the country.