Fluid might not come out depending on where the master cylinder is. If it's under the truck or even height with the calipers, it will not gravity bleed.
If your caliper is slightly dragging, the extra heat will cause it to lock up first, jack up the front and see how the tires rotate. Also as mentioned above, don't assume the side that locks first is the problem, the other side could not be working at all. Have you done a complete system bleed? I know changing lines should have got the air out, but you never know!
The front brakes work as a single unit, same as the rears, so rule out the valves and master cylinder.
The proportioning valve applies the rear brakes first, then the fronts by a spring & valve setup, it also has a safety to block off front or rear in case of sudden pressure lose.
Side to side operation will be equally applied pressure, this then tells you one side has a problem, either air in the system, bad hose, bad caliper or wheel cylinder, dirty pads or shoes, or something sticking. OEM's designed it so it should always stop straight, even with a major problem at one wheel.
Joe