I was at the LAX yesterday (sunday) around 8 pm so nearly the peak departure drop off time for TBIT. And... it wasn't that bad. Traffic flow didn't seen worst than normal despite the lane closure.
But still, If I was going to TBIT, T4, T5, T6, or T7, I would still get dropped by at T2 and just walk to the other terminals. (T1 drop off is usually very congested so not a good place to get dropped off unless you are going to T1)