Old LR Files

If you are asking "Is Lightroom still using this?", then the answer is "No, Lightroom is not still using this".

If you are asking if there could be a reason not to delete the files, then the answer is "Yes, of course there could be a reason why you should not delete these files, but only you can possibly know that reason".

When you say an "old user" I suppose you mean YOU? so these would be your LR files? and is it a catalog?

Normally, when you update or upgrade Lightroom, your previous catalog gets updated also, as with a -2 in the name.

My suggestion would be to see if the "files" are images or data or catalog, and then possibly try to open one "file" to see what it contains. If it is a duplicate or previous catalog of yours and your new catalog is up to date, then you can decide to delete it.  

I generally make sure I. have updated my catalog and my back up catalogs each time I update Lightroom. THen I make sure all my catalogs work by opening them and make sure they contain the folders and images I am used to seeing. Once everything appears in place, I delete any old catalogs so I dont get confused in the future!!!  Hope that helps!

We don't know what is in those files or what else is on your computer, so I doubt anyone across the internet can give a definite answer. However, you can investigate.