It's just a bit odd to me that the driver wouldn't think to update the plate number in the app, or that uber/lyft would be so slow to update it.
I doubt it's a human in the cloud who sees a notification that a driver would like to update their plate number and then adds it to a queue to work on.
I doubt the guy was trying to pull something over on you. I don't drive for Lyft but I feel like it's one of those small easily missed details that's very important to a small subsection of your customers and no one else cares.
Having used Lyft countless times over the last few years I know I have personally never checked the checked that the plate matched.
However, usually that's the way I identify the correct driver. For instance Priuses are the more common car and sometimes it's easier to memorize the first 4 or so digits on a plate than the make/model/color that my driver is driving.
But on the other hand, it's still a small issue at least because in some rare circumstance somebody could use it maliciously.