Perhaps Trajan lamented. Perhaps just an ancient author wrote, that he lamented, because it sounds so nice. However I am sure, Trajan was no young dreamer like Alexander, but a pragmatic roman emperor, who knew, what is possible, and what makes sense from a strategic point of view and what not.
We discussed this already in this thread:
https://www.alternatehistory.com/discussion/showthread.php?t=363731
Trajan would have had a hard time to secure Mesopotamia and Armenia. Actually he already had lost half of Armenia again in 117 and had to sign a rather unfavourable peace contract. Also the fact, that he implemented a parthian client king in Ctesiphon shows, that it was not that easy to provincialize and hold Central Mesopotamia. In North Mesopotamia his legate was still fighting and the desert region of Hatra in between was never conquered by romans.
So I don't see how Trajan not dying would change that much. Perhaps Trajan would try to provincialize and hold northern Mesopotamia like Severus and Diocletian did later.