All airlines offer lie-flat seats in business class flying across the Atlantic these days. Also, newish planes. Most airlines have retired older aircraft during the pandemic (BA sent all their 747s to the desert...) and thy tend to fly the new, fuel-efficient aircraft on long routes to maximize fuel cost savings at todays fuel prices.
However, Lufthansa offers a very mediocre business class product on the A350s they fly to LAX that is in dire need of an overhaul which will not be forthcoming anytime soon. They have 2-2-2- seating with no privacy, plus you get to play footsies with your seat neighbor when seated in the center seats. I actively avoid flying them.
The only - but big - advantage there is that the flight is nonstop, and they don't seem to be charging a premium for it.

If you don't mind trading a connection for a better experience on the longhaul flight, I would recommend:
Swiss LAX-ZRH-MUC. They offer some single "throne" seats (best seats: 4A and 7A!) on their 777 that have very good privacy. Key here is seat selection, so book early to get one of the coveted single seats. The rest of the experience is well above average, too. Food and service are markedly better than on LH.
For a connecting flight, things actually are OK First, ZRH-MUC is a very short hop that takes less than half an hour in the air. Second, ZRH is a nice, compact airport offering a seamless transit experience.

AA/BA LAX-LHR-MUC. Well... I`m kind of biased here as I`m usually loyal to that alliance.
Not taking alliance loyalty, miles and all that into account, this would be worth is to me only if BA had the A380 scheduled to fly the route on your dates and schedules would align nicely so you'd have a short layover. BA's A350 with it's new 'club suite' seat featuring privacy doors is also a step above the competition, seat-wise..
The good: A380 a possibility, otherwise club suites not bad also..
The bad: transiting LHR is, well, not that great of an experience (it's a huge busy airport with a reputation for long lines at security), plus the shorthaul flight is not the greatest experience as well - rather cramped seat for an hour and a half.
If you have no status with oneworld, you'd need to pay for advance seat selection on BA. On the A380, get a window seat but beware, those face backwards which some people don't like. Best seats 53AK on the upper deck.
American's 777-300 is nice, Good seats, good privacy. The service and food offerings are, well, not that great, and the LHR transit experience including the two-hour stint on a cramped BA plane isn't as well.
DO NOT do anything like AA LAX-CLT-MUC or AA LAX-PHL-MUC. You'd be spending 5 hours on a narrowbody in "domestic F" before connecting to your transatlantic flight. On the outbound, the flight from the east coast is too short to catch any meaningful sleep.
The seats on AA's widebodies are OK for the most part, and they have good privacy. Service and food are so-so.

The best experience would flying Qatar LAX-DOH-MUC on aircraft equipped with Qsuites (their new business class product) But I don't think that'd be competitive, price-wise., and you'd be backtracking too much.