Did this just the other day, you no longer need to walk outside (unless you want fresh diesel filled air to breathe, or to partake in a smoke break should that be of your liking).
Upon collecting bags, you walk down a long wide corridor with CBP agents at podiums. At the end, turn right and follow the signs to connecting flights. Once you make a rough U-turn at the end of that hallway, there are agents from the domestic airlines available who can re-tag and re-check bags to their final destination and print boarding passes. After you exit that room, turn Right once again. You will be greeted by a very strict Prosegur agent (black and yellow uniform) who will check your boarding pass. After that, you will continue down the hallway and enter a tiny checkpoint (like 2 lines small) that's only used for connecting flights. After that, there's a series of escalators that dump you right into the middle of the connecting hallway between T4 and TBIT. Turn left for T4, and right for TBIT. It's pretty well signposted all the way if you can't fully remember these directions on the day.
Writing from the Admirals Club lounge in T4 after a fairly confusing transfer from TBIT earlier this afternoon -- wish I had thought to check this thread first. The above detailed description from S80 matches what I saw
except that the tiny checkpoint for connecting flights (noted in bold above) was alas not open. I don't know if this was a one-off or if it is only staffed at particular regular hours. For reasons too painful to belabor, we actually wound up going back through TBIT security (which was a zoo) and then walking to T4 via a quiet corridor on level 5, where the TBIT oneworld lounge is located. In retrospect we should have just followed the signs to T4 and gone through security there. (This is my first time transiting LAX so I'm no expert, just reporting our experience today).