Could someone phrase the sentences in a way a native speaker would write?

I am very lucky. I got into an accident and came out alive. I still have my legs to walk on and to move around with. My leg was not amputated. I am very blessed.

Your original sentences are quite natural. I'm only offering minor possibilities, not corrections.

Fortunately I survived the accident with my legs intact, one badly injured but fortunately not severely enough to require amputation. I was blessed with a recovery that now allows me to walk

Thanks. I agree with your corrections.