Two possible reasons

I finally understand two partial reasons why it was better to meet the father of Lamoni on the road to Middoni than in the city of Lehi. One reason is that in the city of Lehi the king might have felt extra pressure to have Ammon killed. If the scene had played out as it did on the road to Middoni he would have been humiliated in from of his chief subjects. Nothing good could have come from such humiliation. The second reason is that if they had fine to the land of Nephi they may have missed the king altogether as he was traveling (apparently near Middoni).