It does seem that for September all the LHR-LPA are operated by Iberia Express (BA536). Economy fares on most dates at the moment are £45 o/w, which is pretty cheap. Maybe it's worth the OP downgrading to Y (LHR-LPA is £350 o/w in J), and then buying a 3rd seat, and all the BoB you want + lounge access + bags etc....still works out much cheaper than one J seat