I had my BendPak outside all summer a few years ago, and there was no problem. I did have a problem getting a 10' wide 4-post lift in through a 10' door opening. When my BendPak lift was manufactured, they were centering the bottom plate in the middle of the 12" square bottom plate. The posts built after mine are all welded, so the outside of the post is at the edge of the bottom plate, which would have made mine a lot better to get through the door opening. At my old shop, I had an ancient 4-post cable lift outside, and it always worked well. I don't remember the brand, but it was manufactured in the 1950s. There is a local shop that has one like the one that I had (1950s model) that has been outside since 1980, from what I remember, and he is still using it, weather permitting.
I do like the idea of putting a carport covering over it with some panels on the sides and rear. It will keep the weather off of it, but you still need to ensure the cables are protected from condensation. My friend who lives in Apple Valley, California, has his outside, however, he lives in the high desert, so rain isn't much of a factor. The rubber hoses can be protected by plastic hose wrap if the hoses are a concern.