I would not encourage this. The bottle neck and unpredictable aspect of this plan is not immigration, but rather security screening. Even if one has access to fasttrack security this can, not infrequently, be slow, especially if you cross an overzealous LHR screener who selects your bag for a hand search because you didn't realize that small handcream from your therabody amenity kit you threw in your bag classifies as a 'liquid or gel'. It is always preferable to go to a lounge after completing immigration and security, and then one knows how much time you have till boarding. If one picks the arrival lounge option, then will be very short visit as you ideally have to go up to fifth floor for departures and make your way to security line at least 45 mins before scheduled departure, to allow yourself some buffer in case long queue there.

Also to note in your planning is that LH planes, though rarely, will occasionally leave from terminal 2B. I once made an elaborate plan like suggested and had myself in terminal 2A at T-20 only to find out the LH flight was leaving from a B gate - that was the day I discovered it was possible to do the dash from A to B in 8 minutes...