Yes, "the airline LHR" still operates and would be preferable to a train. Choosing a departure that is scheduled to arrive 2.5-3 hours before your flight should be fine.
The Oxford Airline web site recommends arrival at least one hour before check-in opens and I think AA/BA recommend three hours before departure. The advantage of sticking to that is that you are more likely get a sympathetic hearing if something does go wrong.