Wierd starting problem

[pcut]

Driving my '06 LC out in the west desert yesterday lookg at petroglyphs. Aound 100 degrees so AC was on. Drove up and over Johnson Pass and pulled over to let the dog out. Walked around for 5 minutes, got back in the vehicle and it wouldn't start- starter ran for 5-7 seconds and then shut off. Tried it several times- no go. Waited 5 minutes and tried- no go. I put it in neutral and rolled backwards down the hill until I got enough momentum to do a 180 so I was going forwards down the hill. Rolled until I was going about 15 MPH and tried putting it in D- no start. Tried the ignition again and it fired up! Any ideas? I'll try the EFI fuse but does anyone have any other ideas? Searched with no real results.
Thanks.
Tried to correct mispelling but titles won't edit.

 

[inkpot]

Roll start success very unlikely. Requires a second hydraulic pump in the tail-shaft area of automatic transmission. This has been discontinued since the mid 1960s in all of the cars and trucks that I know of. It probably just heat sinked and needed to cool for 20-30 minutes. John

 

[pcut]

I didn't think the roll start would work, but being out of cell range, on a hill that rolled down to the pavement, I figured I had nothing to lose. What do you mean by "heat sinked"? I don't want the same problem out on Cedar Mesa or the Az strip so I'm trying to find the fixs now.

 

[AimCOtaco]

I think he meant heat soaked or vapor locked but that should not really occur at these fuel system pressures.

I wish I could offer something more. What was your fuel load? Could your fuel pump be getting weak?

Next would be to check out all of the immobilizer possibilities, immobilizer is almost always a crank but no-start failure when it occurs.