This verse is difficult to place in context. If we read it as a conclusion to the previous verses, we have Mormon commenting on Limhi's mixed feelings about supplanting his father as ruler of the people. If we read it as the prelude to Gideon's actions, then it would be more suggestive that Limhi requested Gideon to send troops to find his father and return him.
This second is not very likely. If Limhi was not aware that Gideon had intended to kill his father, it is quite likely that Gideon would have made known his intentions. A Limhi shown as not wanting his father destroyed would hardly commission a man who had tried to kill him to provide for his safety.
It would seem easier to see this expedition sent from the city after the return of Limhi's people. Gideon would have been in the city, and initiated the search party as a continuation of his attempt to overthrow Noah. It is therefore quite probable that when the party went to chase down those who fled that they had in mind killing Noah, and that there was at this point no formal recognition of Limhi as king by Gideon nor his men. This must have come after, when events had settled and safety was assured.