After you do the contest, you can chat to all the participants about the results/winner
I completed Lizard treasure a long time ago and I let Xeroth win the contest, the newest (guest writer) contend with Xeroth only triggers Event: Training, second one Talk: Training is not triggering, the only thing is when you go to Rhot and Xeroth say that player should go to Rhot hut and Rhot is annoyed by the lewdness of Xeroth.
I was having the same trouble at first but it seems you need to visit during the morning (I think before 9am which is when Xeroth is still sleeping) warriors on the weekend and then I think go through the 3 options (watch training, train with lizards, spar with lizards) and then talk to Rhot which will trigger the lines 'Where is that lizard...', go to Xeroth and wake him up then visit him (he's gonna be out of his home the entire day) the next day and the training option should be there. Its a very weird way to trigger it I only stumbled on it by accident aha