Does God predestine some people to be saved and others not?
No. The work of the cross was sufficient for everybody, and the door to the sheepfold is at ground level, not beyond anyone's reach. Mankind will not seek God on its own, so God must make the first move, but He has not predestined some to salvation and others to condemnation.
Les teaches that when Adam and Eve sinned they hid from God, and God had to find them. That pattern has never changed: mankind will never, of his own volition, go looking for God; it is contrary to our makeup. God has to make the first move. However, Les explains this does not mean God has forgotten some or, as in extreme Calvinism, already picked out who He will save and who He won't. He disagrees with that because the work of the cross was sufficient for everybody. He uses the illustration of the door to the sheepfold in John 10, noting that the door is at ground level, not beyond the reach of anybody. Yet it still has to begin with God.