If you have stretch marks on your arms, and you lose weight, and do lifting, will your arms look somewhat normal?

Stretch marks are going to stick around. If they are still red, they can be treated with scar/stretch mark preparations and it might do some good. If they are old and silver, they are pretty permanent.

With weight training and weight loss, though, your arms will look firmer and more toned, and more important, you'll be healthier.

I agree, and stretch marks tend to fade over time. Self-tanner is great camouflage.

Yup. But, while stretch marks do fade they never go away. They are little permanent scars. Sometimes the skin is stretched out so much that one's arms do not look normal and they only way to fix that sort of problem is with surgery.

But, I am NOT saying that that will be the case with you. Maybe, maybe not. Everyone is different.