Will I regret booking tickets on arrival day?

Leah,
Do you sleep on transatlantic flights. I don't sleep much at all. When we arrive in Europe, we try to hang on not going to bed until after dinner (say about 7PM).
Personally, I would never book an event the first evening.
If you did book this flight, you could try sleeping a bit in the afternoon, but that could mess up your sleep cycle.

Pprobably --- it will be hard to sit in a dark theater and not feel sleepy. Our pattern now is to take a one to two hour nap on arrival and do a normal bed time of around 10 to 11 pm. We try to stay active during the evening pre and post dinner. Works well for us.

Do you just have one night in London? I would not book an important event on arrival day dut to both reasons you mention.

I don’t know if Six performances sell out as it’s been running a while but you might be able to get same day tickets after your arrival. Someone on the forum who is more into theater may have better info on this as I am truly guessing.

Six is exciting & short-90 minutes with no intermission. That said, I hope you are awake to enjoy it. I usually end up going to bed around 8pm on my arrival day no matter how hard I try to stay awake. Even if I've gotten a couple hours sleep I'm really too tired to do anything but walk around outdoors that 1st day.

I would never do that. As soon as those lights went out, I’d be asleep. I wouldn’t lounge around in your apartment. Get out, walk around, have lunch, explore. Have a nice early dinner, then go to bed. You’ll be refreshed the next morning

As noted above, a lot depends on how well everyone in your group does at sleeping on planes during a long redeye (LAX to LHR is longer than most nonstops from USA to UK). It also depends on to what degree your group are already sleep-deprived before you even head to the airport (something I suspect many of us experience but often don't fully acknowledge...we all figure we will tough it out and be OK).

Remember that any group only moves at the speed (and happiness) of it's slowest, most cranky, most whiney member. Any member of your family of 4 fall into a high-risk category there? You may be tempting fate.

I don't know what "Six" is, but assuming it's some kind of performance in a theater, where you will be seated in the dark, in comfy seats, following a dinner....that sounds like that could be the most compelling sleeping environment that any of your group will have experienced in the previous 48 hours, so don't be shocked if someone only wants to hit the sheets and do it NOW.

Personally, I would not schedule anything at all for that first night after arrival, least of all a sit-down performance in a cushy seat in a darkened theater. I know that me and my spouse would be challenged to stay awake through an early dinner, that's doable for us but after the sun goes down, we are going to be focused mostly on getting some sleep in a comfy, dark place that's not moving. YMMV.

Thanks, y'all! As usual, I know you are right.

I'll join the chorus- not a great idea for an arrival day. You would be lucky to arrive at your hotel much before 13:30, and would be even luckier to have access to that apartment before later in the afternoon. Do you have written confirmation for that early access? Then you need dinner a bit early, since evening performances for Six usually start at 20:00. That would be right about the time I start fighting to keep my eyelids open. But your experiences with transatlantic flights may be different.

Planning to relax at the apartment before dinner is a sure way to zonk out early. And whether you relax at the apartment or get out and about which will help with the jet lag; the odds of staying awake for a play on day of arrival is not in your favor. The LAX to LHR is a rough go...unless you are in first/business. Arriving from the west coast takes it out of you! But, oh so worth it! Enjoy your trip!

The other possible monkey wrench would be a flight cancelation. My flight from Washington-Dulles to London was cancelled back at the beginning of May. I was a full 24 hours late arriving. As a result, I missed a prebooked, rarely-offered morning walking tour I really wanted to take. It was pay-on-the-spot, so at least I didn't lose any money. Four theatre tickets are a different matter.