First of all, it is important to point out that these are not the words of Ammon or Lamoni. Rather, they are the words of the new king, Anti-Nephi-Lehi, as he expresses his gratitude to the Nephite missionaries.
Only the converts to the gospel can fully appreciate the love they have for the missionaries that brought them the message of salvation. Often, they are loved like members of the family. The Lord teaches us that the love between missionary and convert is eternal, And if it so be that you should labor all your days in crying repentance unto this people, and bring, save it be one soul unto me, how great shall be your joy with him in the kingdom of my Father! (DC 18:15). The following story is illustrative of this great love.
LeGrand Richards
"I used to enjoy very much hearing President Grant tell of the Scandinavian Brother who came over to Utah. He had not been taught much about the gospel; all he knew was that it was true. The bishop went to him and taught him the law of tithing. He paid his tithing. He taught him about fast offering. He paid his fast offering. He taught him about ward maintenance (budget) and he paid that. Then the bishop went to him to get a donation to help build the meeting house. The man felt that ought to come out of the tithing, but before the bishop was through with him, he paid his contribution toward the meeting house. Then the bishop went to him to get his son to go on a mission. The good brother said, 'That is the straw that breaks the camel's back. He is the only child we have, and his mother can't miss him.' Then the bishop countered, 'Brother so and so, who do you love in this world more than anyone outside of your immediate family?' He thought a few minutes and said he guessed he loved that Mormon Elder who came up to the land of the midnight sun and taught him the Gospel of Jesus Christ. Then the Bishop countered, 'Brother so and so, how would you like someone to love your boy just like you love that young Mormon Elder' The brother said, 'Bishop, you win again. Take him. I will be glad to support him in the mission field.'" (Just To Illustrate, p. 52)