Can I lose weight by sweating?

It depends if you're looking for temporary or permanent weight loss. Assuming you're interested in improving your health, the answer is no, you can't lose weight by sweating.

When you sweat, all you're losing is water weight in the form of perspiration. Your body (if you're in good health) is very good at balancing the amount of water you hold.

Once you sweat out a lot of water, your body detects this and the next time you drink a glass of water or eat anything, you'll quickly absorb the weight you lost through sweating.

This isn't to say that you shouldn't sweat. If you're sweating, that means you're exercising and if you're exercising then you're burning calories. Burning calories, unlike sweating will cause permanent weight loss.