He should have been asked at LGW whether he had passport, pills, keys, PCs with him.

In this situation he needs to tell the CSM since there is a small risk that BA will be fined if he turns up at Schengen without a passport (though unlike Germany I believe Spain only very rarely does this). The CSM should liaise with the ground agents to retrieve the bag directly upon arrival. If that doesn't happen then if your colleague has other paperwork to support their identity (driving licence?) then there is a good chance the border officer will just wave them through. Otherwise it may lead to some significant hold up while an officer is found to go down to the baggage hall with your colleague and then retreat back to the computers to ensure due process is followed. If he is a EEA citizen then there is an underlying provision under the relevant treaties to allow entry into Spain, there is a specific clause that says that failure to produce valid paperwork is not in itself a reason to deny Freedom of Movement.