Security I'm only aware of an above ground walkway between Terminals 6 and 7. I believe all LAX tunnels are closed at this time.
FlyerTalk Airports/Los Angeles/LAX tunnels closed permanently!
Unfortunately, you will need to exit Terminal 7 (or Terminal 6 if you use the walkway) and then re-enter Security at Terminal 4. In your case, there's no real advantage to using the walkway, IMHO. Terminal 7 to Terminal 4 should be a five to ten minute walk, all on the same side of the street, without crossing any streets.
FlyerTalk Airports/Los Angeles/LAX - do you have to exit security to change terminals?
The best thing you can spend on your children is time.
[This message has been edited by MRLIMO (edited 12-08-2002).]