There are 4 examples of a lose-lose situation.

Lose is just a word.To lose is to suffer a loss, to be deprived of, or to fail to keep possession of.

Things that are not tightly fitted are referred to as loose.They loosed the dogs on the invaders, but the word "release" is rarely used this way.It also has a sense of large, which is mainly confined to the idiom on the loose.loosen is the best choice when you want to partially release or relax.

I didn't have much to lose when I first arrived in London because I was so young.TheGuardian

Imagine what the competitive landscape would be like if the company were able to sell its own product.Variety

Attorneys want police to be alert to the possibility of a suspect on the loose with blood.The Roanoke Times.

Why is this a common mistake?I am not a scholar when it comes to writing, but this is the one that drives me crazy when I see it online.