The Lace Museum looks like is still there.
Unfortunately those handcraft traditions are largely lost, probably with my grandparents' generation (my grandparents were born in the 1890s). The island is also largely uninhabited now, as few residents are left.
While browsing the net on this topic, however, I found this YouTube video from QuattroColonne (4 Columns), which is the media outlet of the Perugia's School of Journalism. The video shows a group of 'volunteers' from Tuoro Sul Trasimeno (a town on the lake) which are trying to keep the tradition alive.
https://youtu.be/0FdF8-S3go4?si=6UQNZfGxlBKYtgw0
If you don't speak or understand Italian you can add English subtitles to any YouTube video, no matter which language.
Just tap the screen (if Ipad) or hover the mouse cursor on the video (for desktop). You will see the Close Caption icon (two small CC). Click on that to activate Close Captioning and you will see subtitles. The subtitles will appear in the original language, so to have it translated in English, you will see the setting icon (looks like a gear) next to the CC icon. Open the setting and select AutoTranslate, then select the language you want it translated into (English). Et voilà, the Italian video will have English subtitles at the bottom.