As long as they put them in the leader slot on a certain table they'll be available to borrow.
However; you have to be in the same table (i.e Cantina, LS, DS, etc). They don't just universally show up.
Also, if you have used that Ally to borrow a character in the last few hours you are unable to borrow from them for a fixed amount of time. I don't recall the exact amount but I think it's a couple of hours at least. Just keep re-entering the node to choose an ally and it's like refreshing the Arena screen.