It doesn't matter if you use UK address (you get an LH-branded M&M card) or a CH address (LX branded) for anything mileage-related.

Whats your main flying pattern? Cheap economy long haul? Then M&M will be about the worst program you can wish for. You'd have to fly around 15 times round trip to Singapore (for example) to just make their "Frequent Flyer" status (which nowadays only gets you into LH/LX/OS branded lounges, ie mostly access only in DACH (and not even in Basel anymore)

Becoming SEN in Economy is close to impossible, unless you fly on full fare tariffs (for work)

However, if you fly a lot of long haul in Premium Economy, things might turn quite well on the Swiss/M&M side. 100% earning (plus 25% once you're FTL), which means you can relatively easy get FTL.

Or you fly a lot of cheap (K/L) classes within Europe, then 15 Round Trips (30 segments) will ALSO get you FTL status. Funny enough, 15 RT within Europe on 99 CHF fares will give you FTL status just as fast as 15 RTs to Singapore.. talk about sense Route it through FRA/MUC, and you're down to 8 RTs for FTL status..

That said, it really depends on which booking classes you'll be flying. P (Cheapest business fare, often not really cheap Ex-ZRH) gets you just as much miles as.. tada.. Cheapest Premium Economy fare.. no, it doesn't make sense, but that's how LH Group runs their show.

If you fly a lot, on expensive fares (or in Premium Economy on LH..) then M&M makes sense. If you fly a lot on cheap-cheap European destinations, then M&M for FTL makes sense too.

If you fly a lot long haul in cheaper Y, I'd check what other Star Alliance program would still get reasonable amount of miles to hit Star Gold status there.

Basically, there is no universal answer to your question, as it depends heavily on your future flying activities.

If you're flying in Y, I'd avoid LX to be honest, especially long haul. Their product is either outdated (A340), or really cramped (B777) - changing in FRA onto a Y+ product from LH is a good alternative I've found to both have a reasonable good product, getting decent miles, as well as good prices (They've been running sales as low as 650€ in Y+ to long haul destinations, but you can snatch them regularely for below 1000€, which is still a good deal)

If you're allowed to fly C (from your company?) then LX of course is a good product for direct flights, but your company will pay through the nose for it. I know a few companies sending their staff to fly longhaul Ex-MXP on EK, and that was before the new Gotthard tunnel cut down time even more. Of course, EK only offers New York from MXP westwards, so probably that's not a good option for you. C (and F) regular fares Ex-Switzerland on direct LX services are, in two words, silly expensive. If you have an employer paying for them, great for you, otherwise plenty of alternatives exist.

Regarding Switzerland, we're not spoilt with great Credit Card opportunities. The new Cornercard Diners card gives 1 mile for each CHF spent, which is as good as it goes. Alternatively, Amex from Swisscard is 1.5 for 2 CHF spent. Both helps to preserve your miles (they won't expire after 3 years if you're not FTL at least)