You have 3 options. To be honest it doesn’t matter that much. But the more you enlarge the more it matters.
Option 1 output from lightroom the native file size and send it for printing. Let the printer enlarge it. To be honest this is probably as good as anything.
Option 2 let lightroom enlarge the file the size you want and the dpi that the printer recommends. this will remove any file size warnings but probably result in the same results as options 1
Options get really obsessed about how to enlarge it. Buy a copy of genuine fractals and use that. Or try something like the Roman Johnson method which will require photoshop and I can’t find the link to at the moment. This might help in for extreme enlargement
Now for a useful hint
You need to crop a small part of the picture and print it at the proper size. Then you can see if the quality is good enough for the use you will put it too.
This takes a bit of thinking about in Lightroom. Infact although i could tell you how to do it in photoshop but not lightroom. maybe some one elase know