LH business class (even if you get the new version, which is not certain) does not offer a flat horizontal bed. It is a 'flat but slopes down to the floor so you slide slowly to the floor during the night' bed.

The sleeper service sounds like a bad idea but I am a convert. The meal I had in the JFK lounge last month was better than anything I have ever had on board, and they do have light meals on board and breakfast. And when you arrive you can use the BA arrivals lounge for a full breakfast, shower etc.