Just FYI - if you are searching for information the web address is: https://www.puccinimuseum.org/ (Guide book says: https://www.puccinimuseum.it/)
Even if you aren't a huge Puccini person, it's a good rainy day activity. It's pretty close to the Palazzo Mansi if you want to see how the 1%ers of Lucca lived. There's a good pizza al taglio place "Alice" around the corner from Puccini House on Via S. Paolino
The Puccini museum in Lucca is the house where Puccini was born, but due to problems better not discussed here, he did't live in Lucca anymore since a short time after the beginning of his career. The Lucca museum houses souvenirs coming from the composer's family through his daughter-in-law (that he didn't live enough to know).
The house that Puccini built himself is the villa in Torre del Lago, near Viareggio, where the operas from Madama Butterfly to Gianni Schicchi were written. This villa was set to be his main museum shortly after his death; he is buried there, in the wall on the back of the piano he used for composing.
Puccini's very last opera was written in a futuristic villa in Viareggio; presently in bad conditions, so it can be visited only on special occasions and with guided groups, usually a couple times per year.
also, there is outdoor performance space at Torre del Lago where Puccini's works are performed. It's seasonal so check availability.