It is not entirely clear in the present text whether those being promised eternal life are the Lamanites who embrace the faith or Mosiah’s sons who serve in faith. It is axiomatic that those who accept the message of salvation and conform their lives thereto will eventually inherit eternal life.
Of special interest in the context of our present story, however, are the many passages that promise eternal life to the faithful missionary. One of the first revelations given in our dispensation announced that those who go forth in the name of the Lord must serve with all their heart, might, mind, and strength that they might stand blameless before him at the day of judgment.
The revelation promised those so laboring that through such service they may lay “up in store” that they perish not, but bring salvation to their own souls (D&C 4:2-4). That is simply to say that we serve to work out our own salvation. The sons of Mosiah were very much in need of the opportunity to render such service. See also commentary on Mosiah 27:32-37.