I understand, getting rid of unnecessary travel time always makes more sense. Assisi will have to wait!
I would suggest to enjoy Lucca, renting bikes to do the wall circuit several times, it is very enjoyable and weather should be great in September for it. You can make a half day to Pisa for sure, to see the tower, but Florence will require a whole day. If you don't want to try to fit in too many things, I'd just suggest spending time nearby.
For example, another recommendation would be to take the bus that takes you into the hills nearby to see some of the villas that surround Lucca. We really love Marlia and it is easy to get to. Here is my review, with info on bus toward the end for getting there:
https://www.discovertuscany.com/lucca/villa-reale-marlia-near-lucca.html (bus 59 from Piazzale Verdi, stop right in front of the villa entrance). You can easily spend a whole half day there, especially if you want to enjoy visiting the villas and gardens without a hurry.
This article lists a few more:
https://www.discovertuscany.com/lucca/historical-villas-in-lucca.html
If you'd like to go to the beach a day, you could head to Viareggio, also easy to reach by train, and walk to the seafront. There are lots of bathing establishments where you can rent chairs and sun umbrella, as well as a "free" area of beach to the south where you can plant a towel on the sand and enjoy. Most people do carry along their own sun umbrellas, you'll be able to tell once you're in that area by the mish-mash of umbrellas that don't match anymore
I am sure your walk down the Francigena will be lovely, I'd love to hear back how that goes after you do it!! I imagine you're doing it with a group, so would love feedback on the tour and how well it is organized, whether the pace is good and how the lodgings are set up. Aside from knowing more, it is something that I'd like to do as soon as my own kids are a little older (my youngest just turned 3).