Richard - I'm afraid you're not completly updated on The Virgin Group.
Years ago - I forget when - Virgin Group sold 49% of VS to Singapore Airlines. the partnership did not give the desired effects, for either airline, and SIA has stated that they want out, and Virgin wants to buy the share back. That this hasn't happened yet, must be because there's an argument over price. Virgin Group's strategy all along has been to partner with other companies, and not neccessarily have a controlling interest in the Virgin-branded companies. The record label - that stated it all - was sold more than a decade ago, and still provides Virgin Group with some nice reoyalites I assume.
As for Virgin America, Virgin Group was orced to water-down it's share in the carrier due to restrictive American ownership laws (land of the free, yeah right...). Virgin Blue is owned 25% by Virging Group. The carrier was the target of a hostile take-over two years ago, but in the end the company wanting to take over Virgin Blue was itself taken over, and Virgin could hold on to its quarter-share of the airline.
I am a bit puzzeled by your remark that Virgin Atlantic is one of the carriers that will disappear. VS posted a better-than-last year Q2 result (partly due to the trouble at BA's T5, but still).
LH wants bmi for the same reasons that VS - access to Fortress Heathrow, but for VS it will also give it feed (on the short-haul routes that are deamed valuable enough to be kept). LH (as well as SK) has been said to have an option to buy the rest of bmi should Sir Michael Bishop want to sell. Thus far he has held on to the carrier. He is the majority share-holder (50% + one share), and he is a shrewd business-man. An option to buy is (as SAS knows in the case of airBaltic), no sure thing. And, it is always possible to get out of old agreements...