One should avoid a connection with a change of airports i.e. LGW to LHR. At LHR a lot of walking. Does your friend have to pick up her bags or are they taken care of by BA? Just to get from Terminal 1 to Terminal 4 at Heathrow it takes me about 45 minutes++++. So conservatively I think you must count 1 hour to get into the bus and leave + 1hr 15 min to get to LGW. However the BA LGW terminal is great! It's relatively small and not too much walking to the plane.