Runner Interference to first
 

BR swings for the fences and hit a dribbler about 8 feet out, F2 approaches and begins his throw to F3. BR is not in the running lane, and catcher throws a low throw to first where F3 was unable to pick it, thereby allowing runner to be safe. The ball never touched the runner, but from the PU angle, he could clearly see he was running in fair territory. Is it interference with the BR being struck by the ball?

Depends on the code.

In FED, you can rule the runner caused the low throw and get RLI. Same in NCAA.

In OBR, it's just a bad throw and the runner is safe.

(I'm assuming the throw did NOT actually hit the runner and that the throw was in the dirt.)

In addition to the other answers: If the runner wasn't to the running lane yet (halfway to 1B) then it isn't interference no matter where he's running.

This was the first thing that came to my mind as I read the OP.

The other issue is that I don't know that I've ever seen a player make a low throw to try to avoid hitting the BR. Usually the issue is that the catcher or pitcher will try to throw over the BR to get it to first base, which to me is an easier situation to say the presence of the BR outside the lane impacted the throw. Not saying the PU can't make that call just because it was low, but I'm having a hard time picturing the play with a low throw.