Different classes inbound/outbound is completely OK. But easily booking online may be another matter. If just BA, this is very easy, but if you want to mix BA/JL and classes, I would recommend either calling BA to price up, or some travel agent. JL call centre in London is extremely polite, but rather bizarre...they only issue paper receipts, for example.
I have to be honest, in Y, flight crew may not have a huge amount of time for inquisitive small people, which is a shame, but the truth of the matter. But for sure, BA will be vastly superior to JL in this regard.
Good luck!
tb