Sometimes when I get too overheated from walking around town, I'll duck down under either Baluardo San Martino or Baluardo San Paulino and enjoy the cool subterranean air, the wonderful arches, and the temporary art exhibits.
On the other hand, sitting at a street-side cafe and people-watching is another way to chill out. It is like being inside a foreign film with no script and no director - life unfolding is the only theme.
Turandot, a cafe on Piazza San Michele is washed in sunlight as it faces south across the piazza. They seem to have an ethos here (broadly in Italy not just Lucca) that once you sit down and order something - anything however large or small - you own the table until you are ready to leave. No bum's rush to vacate when you are finished, no guilt, just relax and enjoy. I can do that - but I do need more practice.