Rumour has it that a deal with Lufty was being discussed just before Sept 11, but it fell apart initially because of the Pension Fund shortfall (is there one?). presumablly the events in Sept put further negotiation onto the back burner.
It would certainly seem logical, Lufty have publicly stated they have no intention of creating a 'Low Cost' airline, why bother when bmi already exists in that form. When British Midland were rumoured to be about to change their name last year, LBA was suggested, 'Lufthansas Budget Airline'