Mosiah 21:21 - 21:25

Mosiah 21:21 For they were desirous to take them that they might punish them; for they had come into the land of Nephi by night, and carried off their grain and many of their precious things; therefore they laid wait for them.

These priest were still on the lose and were coming into their fields at night to take grain and steal whatever was within their grasp.

Mosiah 21:22 And it came to pass that there was no more disturbance between the Lamanites and the people of Limhi, even until the time that Ammon and his brethren came into the land.

This uneasy peace was holding when Ammon and his party showed up.

Mosiah 21:23 And the king having been without the gates of the city with his guard, discovered Ammon and his brethren; and supposing them to be priests of Noah therefore he caused that they should be taken, and bound, and cast into prison. And had they been the priests of Noah he would have caused that they should be put to death.

However, Limhi thinking they were some of the priest of Noah who they had been on the lookout for, they were taken bound and thrown into prison and were slated for death.

Mosiah 21:24 But when he found that they were not, but that they were his brethren, and had come from the land of Zarahemla, he was filled with exceedingly great joy.

But when Limhi found out that they were from Zarahemla, they were thrilled to know they were not alone in the world.
[Still wonder why Ammon did not speak up immediately when captured? He could have saved himself some jail time and maybe the anxiety over thinking he and his friends would be executed. But maybe they were told not to speak or they would be put to death immediately. Maybe it is custom that you only speak to a king when given permission.]

Mosiah 21:25 Now king Limhi had sent, previous to the coming of Ammon, a small number of men to search for the land of Zarahemla; but they could not find it, and they were lost in the wilderness.

The reason that king Limhi were filled with joy was that Limhi had sent some men out to try and find Zarahemla but they had gotten lost and could not find it.
[It is remarkable that these lands were not that far apart and you would think they kept up some kind of correspondence with each other. Or at least the way between the lands would still be known. It was only 70 or 80 years since they came to the land of Nephi.]