What happened to King Limhi? After he & his people escaped to Zarahemla, he's baptized & seemingly fades away.

Here is a very important principle to keep in mind while studying the scriptures:

1 Nephi 6

3. And it mattereth not to me that I am particular to give a full account of all the things of my father, for they cannot be written upon these plates, for I desire the room that I may write of the things of God.
4. For the fulness of mine intent is that I may persuade men to come unto the God of Abraham, and the God of Isaac, and the God of Jacob, and be saved.
5. Wherefore, the things which are pleasing unto the world I do not write, but the things which are pleasing unto God and unto those who are not of the world.
6. Wherefore, I shall give commandment unto my seed, that they shall not occupy these plates with things which are not of worth unto the children of men.

Scriptures should not be approached as historical or biographical expositions. There are too many things left out that would be satisfying to the historian. They must not be used to figure out geography. All unnecessary details are left out. All of that are “the things which are pleasing unto the world”, and “these things”, says Nephi, “I do not write”.

Even the gospels should not be regarded as biographical nor historical.

The scriptures, however, fully meet their design. They effectively “persuade men to come unto the God of Abraham, and the God of Isaac, and the God of Jacob, and be saved”.

This was Saint John’s view.

John 20:31 But these are written, that ye might believe that Jesus is the Christ, the Son of God; and that believing ye might have life through his name.

There was all kinds of biographical, geographical, cultural and political items that could have been included in the gospels and in the Book of Mormon. There were many things that Jesus did that could have been shared. But all those things were beyond the design and purpose of the written word.

John 21:25. And there are also many other things which Jesus did, the which, if they should be written every one, I suppose that even the world itself could not contain the books that should be written. Amen.

I try not to get distracted by what isn’t there written. I try to use the scriptures to extract myself from the world and those things that please it.

King Limhi

Those things which would answer your question regarding Limhi are engraven on other plates:

1 Nephi 9:4 Upon the other plates should be engraven an account of the reign of the kings, and the wars and contentions of my people; wherefore these plates are for the more part of the ministry; and the other plates are for the more part of the reign of the kings and the wars and contentions of my people.

I think Limhi would be pleased. I recall the words of John the Baptist.

John 3:30 [Jesus] must increase, but I must decrease.

Let’s play our minuscule part and then gladly leave the stage that God alone may be glorified.

2 Nephi 12:17 And the loftiness of man shall be bowed down, and the haughtiness of men shall be made low; and the Lord alone shall be exalted in that day.