Yes you will have to clear immigration and pick up your bags at LAX to take them through customs.

I am not sure if there is a bag drop just after customs for connections - I have a feeling there is and it will save you having to walk around to T4 to check them back in.

There is also a separate quieter seucrity point in TBIT which you can use rather than going to T4 after dropping bags as noted here https://liveandletsfly.com/best-kept-secret-lax/. Once through, you can walk across to T4 airside.

However, I would say LAX immigration is notoriously bad, and in your situation I would not feel comfortable at all with 1.5 hours, even assuming your flight arrives on time I would say there is a significant chance you will miss your onward flight.