Not that I’m aware of, sorry!
There is a way to see it in your photo library, which may give you a clue as to where you took it. Or the location info if you have it turned on.
Long press/Customize/hit the 3 buttons in the lower right/Show Photo in Library
I do have location turned on however I have thousands of pics and it is while they are popping up on my phone that I want to know location. I think it would be a good addition
Here’s another data point on Apple’s poor implementation of Lock Screen photo shuffle. I tried setting up a lock screen with shuffling photos on my wife’s iPhone (also with 16.3.1). It only offers Nature and Cities. No Pets, even though there are dozens of photos of our springer spaniel (no longer with us ) in her camera roll. And there’s only 1 Person offered.
However, in an amazing bit of serendipity, the single person available on her phone for the shuffle feature is me. And the only person available on mine is her. How clever is that? Coincidence? Or perhaps due to the fact that we are part of iCloud Family Sharing?
That’s really cute! I’d love to test that but my SO is not interested in the shuffle feature and as you know, I can’t see anything but nature lol!
On the flip side, I’ve gotten to see some pix on my phone that have been hidden for a few years :)