I haven’t heard anything about them in a decade or two.
Good morning. When I saw your question, I wondered too. Here is what I found:
http://luciearnaz.com/biography.html
http://www.lucy-desi.com/fan-central/desi-arnaz-jr/
Lucie Arnaz is involved in music, as shown here with her projects from 2010. Note the appearance by Desi Arnaz IV.
Neither one of them has to work. They have a lot of money.