How do I recover a lost photo on my iPhone?

If it was not deleted from the Recently Deleted album and it has been less than 30 days since it was deleted, then you can recover it here:

How to recover deleted photos on your iPhone, iPad, Mac, or Apple Vision Pro - Apple Support

Otherwise you would have needed to save the photo in an external location to prevent loss.

“How do I recover a lost photo on my iPhone?“

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Locating a Lost File:

If it is “lost” as in “cannot be located”, then go into the Files app, and type a keyword of the filename. Point being: It doesn’t necessarily have to be in the Photos app; just stored somewhere else.

I completely agree with Jim: if your photos are permanently deleted, there is no way to recover them from your iPhone. There are some of the third-party iPhone data recovery apps who claims to be the best, and in my case, I tried many, and I gave up on recovering anything after permanently deleting data from my iPhone. That's how secure an iPhone is! You have a flaw in yourself, that's why you lost your iPhone photos, but once deleted, no superpower can track and bring back your data.