This has been played from so many angles depending on the author/director. If Holmes didn't exist, Lestrade would be considered a great detective on his own merit. In some productions, he has no covetousness toward the honor but in many he shows second chair envy. Not intending to influence but I love the non competition version who honors Holmes as friend and colleague. There can always be conflict even in that but in so many shows they play it like he wants to dismiss Holmes and that is just not how the original was written, but that is relying on my memory of it.
Your rendition feels right. I can totally lock on that pic.