There are sidewalks the whole way. LAX is bizarrely easily walkable (so very not-LA) once you understand how, but it's not obvious at all until you do it a few times.

You want to walk east out of the north side of the horseshoe and then all you have to do is walk across Sepulveda.

So if you're already on the north side (T1-T3) just head east, walk past the LAXit lot, push the button at Sepulveda, and you're there when you get across the street. It's about 0.3 miles from T1.

If you're on the south side it's more complicated because the construction makes getting across the horseshoe more confusing. You can either take the bus to the LAXit lot (get it on the inside curb closest to the terminal) and follow the directions above, or walk east toward T7 and then follow the signs for walking to the LAXit lot, then turn right and cross Sepulveda. There's a more pleasant and slightly shorter way through the flagpole park, but it's less obvious when walking from the terminals.

I've been parking a lot at QuikPark, which is right behind the Hyatt and shares a shuttle, and I've always walked to T6. It's a very easy walk - I've done it with quite a bit of luggage even. I used to walk to Lot C all the time (surrounded where the Cell Phone Waiting Lot is now) and it was a nice walk. Crossing the Vicksburg bridge when planes are coming in is really cool - they're *very* close.