Alex who expended too much energy in the fight sat down at the edge of the spring. He wasn't sure what had happened in the end, but hearing Lyner tell him that they won surprised him.
There were a lot of coincidences that happened, and Lyner wasn't even taking it seriously for the first nineteen minutes.
Also even though he said he was taking it seriously near the end, he wasn't really trying to kill them or anything his only objective was to capture them. The difficulty of killing a target and capturing a target were totally different.
Killing a target was easier since one can do that even if he is weaker than the target, since there are a lot of factors in killing, like equipment, location, weather, and other such details. If everything was placed in the right order even an untrained child could somehow kill Alex.