I’ve always thought the exact same thing, the coats look very similar and giving that Arthur took his father’s hat I wouldn’t be surprised if he was given the jacket as well.

The Rebel would make sense since Lyle was a known outlaw and violent man, I always speculated that he might had something to do with Beatrice death but I could be wrong.

I would say its safe to assume this jacket is Lyles, as the wear on it is significantly higher even when compared to arthurs other coat. i never really used this one but now that im looking at it there's very little doubt in my mind.

The collar is bigger on Arthur though

R* didn't put too much effort on making Lyle's clothes because they ain't important, they only wanted to let us know how he looked like.

Yes that coat likely belonged to Arthur father