I took Luke’s lack of a direct third lesson intentional on his behalf (and on the meta narrative’s behalf). Her third lesson is doing things on her own. Her failures (to try to bring Kylo back) are hers to discover, not follow the prescribed jedi way; whatever that one theoretically would be.
In a way, it’s similar to how Obi-Wan “cannot interfere” with Luke vs Vader on Bespin. That was a teaching moment for Luke, and now it’s an unspoken teaching moment for Rey. It’s for them to get through. They can’t have their hands held anymore, and both Rey and Luke learn terrible truths about themselves and their heritage because of this.
Or maybe her third lesson is to realize that she will not be the last Jedi, and that she indeed has purpose in that sense?
It’s now up for interpretation now that the original third lesson scene is deleted, and I think it’s much better that way. Besides, Luke and ghost Yoda’s philosophy is to look past an old set of Jedi books (ie, don’t just follow a dogmatic list of three lessons.)
Point is, I don’t think it’s totally necessary to include talks of Luke’s third lesson in TROS. That was a TLJ thing, and, to me at least, it’s over with. But if everyone else thinks it works and is necessary to round this story out and whatnot, then go for it. I feel like they would have included him saying it in the actual film if it was totally necessary here. (unless they just forgot and would have included it…)