When I open a document, how do I delete it on the open page? What if I am unable to find it again in my files.

I somehow opened a document that is 15 years old. Not sure how I found it but would like to delete it, without trying to figure out how I found it.

If you click File > Properties , select the General tab and, under Location, you can see where it is stored. Make a note of the name and navigate to it in your file manager and delete it from there. See File Management in the wiki

Do not try to delete it while it is open in LibreOffice as there is a good chance that you will crash LibreOffice.

In addition:

File management