Audcaity will take in your MP3 file and covert it to Audacity project format. Agter you split it up and then export to MP3s you will compound the data loss caused by conversion to MP3.
Some of the tools on that page I linked to will cut the MP3 directly - with no additional compression damage.
If you still want to use Audacity and LAME for other things…
Maybe I didn’t give you complete instructions - Don’t double-click on the Internet link. First click and download Lame_v3.99.3_for_Windows.exe. Then once it’s on your computer, run it.
Hopefully, LAME will be built-into the next Audacity release! I know the developers are working on that now that the patents have expired.