I think you'll find that BA merging with LH would lead to a monopoly enquiry which would almost certainly be vetoed by UK, German and EU regulators
Why would that be the case?
LH and BA are not the only carriers on the London-Germany/Switzerland/Austria/Belgium routes for a start
Also LH does not have any hubs in Spain or the UK
Then there is the matter of LCCs
The bigger problem would be the question of alliances