The answers can be found in the LA forum.

All of the terminals are isolated, so in general you have to leave security to switch termials. There are some exceptions, but T1 is not one of them.

To get to T3, after you leave the T1 secured area, head to your right and it'll be a 5-10 walk to T3.

To get to T7, you can continue walking around past T3 (LAX is in the shape of a "U"... T1 and T7/8 are at the "ends" of the U), which will be like a 15-25 min walk.

OR you can go straight ahead, cut through the parking lots/garages, and make it a 5 min walk.

OR, you can just take one of the terminal buses (boarding downstairs on the arrivals levels, on the islands.)

Good luck.