Here is what you need to know. VS uses TBIT for arrival and T2 for departure check in (but operates from TIBT) at LAX.

On inbound, if you don't plan to check luggage, the AA flight with 3 hours should be plenty of time. If you have global entry and no checked luggage, you will be landside in about 15 minutes after the plane park at the gate. If you don't have global entry, you should still be able to beat the crowd since you are in J... budget maybe 30 min to clear immigration. So definitely take the earlier AA flight if you don't plan to check luggage. Once you are landside, I suggest you do online check in with AA and use the TBIT ground floor TSA which offers air side passage to T4. Or you can exit the building and walk to T4 which is to your right about 30 meters and do in-person check in with AA.

If you have checked luggage, I would consider booking the later DL flight. VS and DL codeshare so VS should be able to issue boarding passes and tag your luggage to LAS. Same timeline as before but I would add 30-40 mins to collect luggage before custom. Once you clear customs (simple walk-through if nothing to declare), you can re-check luggage at TBIT (to the right once you go past the custom checkpoint, but before you exit to landside). This is where booking DL will make it easier with checked luggage because you can just drop off your bag and then walk to T3 TSA directly, bypassing the DL check in. T3 TSA is to your left about 70 or 80 meters walk.

On outbound, I would book at Delta flight. DL will check you in at LAS and issue boarding pass for LAX-LHR and tag your luggage all the way thru to LHR so no need to pick it up at LAX. You will arrive at T2 or T3 and proceed directly to Delta One lounge, or VS lounge in TBIT, or to the gate if you prefer. There is secure air side passage from T2/3 to TBIT where VS will depart physically. You probably want to give yourself at least 1 hour to connect at LAX outbound but you can do it in less time if staying airside the whole time.