I see what you mean, now. For some reason, I thought the LT user name was taken from the Steam user name. It is not.
Thing is, Lestrade's doesn't store Steam user names at all, it gets the Steam ID through the API, and then stores that.
When logging in, one of the response elements has the proper ID in it. That's what I store, and then I move onto other things.
I'm sorry that I can't help in this regard.
I could, ideally, add some code to turn a Steam user name into a Steam ID on the fly, by doing a request internally, but it'd imply doing some exchanges between LT and the Steam server, and as you know, there's a limit to how much I can do per day, so if someone decided to write a quick script to request a Steam ID from a random, non-existent Steam user name, they might be able to get Steam to softban Lestrade's for a while, and make it work less reliably.
What I'd suggest is to look into your own side, see if there's a way to get an ID from a user name, perhaps with some quick Ajax code. I could even help you with that, if you're not sure how to do it.