MP3 compression

Does MP3 compression work in similar principle to JPEG compression? In other words, editing a file and then re-saving further compresses the file losing even more data? I am familiar with graphic file compression – not so much audio files. If I import an (voice lecture) MP3 file into Audacity, make edits, then export as MP3 again, the quality will be less than the original?

Audacity 2.1.0; 10.12.3

Yes. MP3 is a “lossy compression” format.
As with JPG, the damage can be minimised by choosing a low compression (bigger file size) setting, or better, by exporting in a lossless format such as WAV.