It is not the Lannisters. Cersei may hold the Throne by force on the show, but she has no legal right to it.
As to which of the collateral relations would count, I think there would be a variety of competing claims. The Florents would press their proximity through Shireen, the Estermonts would probably argue for a claim proceeding from Robert, some might back a Targaryen as a way to get back to a clear line of succession, etc.