Subject in English

Solution 1:

You are correct in thinking that this could cause confusion, as the second "he" could mean either of the two previously mentioned people. To avoid this, I would explicitly state the subject of the second one, like this:

"Lon wrote a letter. He sent it to Jacob. Jacob was excited."

Another way to disambiguate, as @Janus Bahs Jacquet mentioned, is to use relative clauses. In this case, the subject of the clause would be relative to the preceding subject:

"Lon wrote a letter and sent it to Jacob, who was excited."

or...

"Lon wrote a letter. He sent it to Jacob, who was excited."