Ideally you'd just have a carry-on, clear security at B, go to the lounge, then head to E whenever you want to be there. I'd budget like 10-15 mins at a normal pace to walk that airside - and yeah I'd do it airside vs reclearing security. The walk could be longer or shorter depending on where in E you need to get, but I think the gates are all still shared so you may not know until the day of the flight. If you have a bag to check, you'll have to do that at E. Totally your call if you want to go up and back. There isn't an airside shuttle. If you have the free time and want to check the place out, no reason not to.

Do you otherwise have access to the Lufthansa lounge with your flight? Their lounge isn't bad. OMAAT has a recent review up if you wanted to see pictures. It's not a windowless dungeon like the AF lounge.

This is not what you're asking, but just to throw it out there, lounges seem really crowded these days. I haven't tried a Chase lounge yet, but if there's any way to know the crowd level before going, it's worth a look. It would suck to walk all the way out there and have to stand in line.