I only fly domestic BD a few times a year on cheapest available tickets. Until recently an E class domestic flight on BD earned 500 miles with M&M and 300 miles with DC, but just before my last BD flight I noticed that an E class domestic flight now only earns125 miles with M&M but sitll earns 300 miles with DC. Needless to say I credited the last two BD flights in E to my DC account. You can argue 300 DC miles are worth more than 500 M&M miles for redemption but that's another topic.

As Mr H has pointed out if you fly enough to get to silver status but not to gold status you are probably best off joining the programme of the airline you fly with most often as that's the only one you'll get lounge access for.

In your case although you are LH FTL (Silver) if you fly mostly from LHR on BD in Y you are not getting access to a BD lounge. Time for a rethink.