So, I'm trying to plan a series of trips on several carriers, almost all of it works out except one bit, as follows:

I could arrive into LHR on a LH flight and depart that same morning with BA... this would be a Sunday morning, if that makes any difference

Inbound: LH2470 arrives T1 at 08.30
Outbound: BA0778 departs T5 at 10.35

a) Lunacy to even attempt?
b) 50:50 chance of it working?
c) "Go for it... you'll be fine "?

Hand baggage only in case you're wondering - so if I've checked in online I should be able to get an airside transfer via Flight Connections at T1, shouldn't I?

Would have to be booked on two PNRs ... so I understand if LH2470 is late, I'm screwed... but my alternatives aren't looking that great.