We will be traveling by rail through Pisa for a day trip; is there any secure luggage storage while we walk the City or do we need to plan to bring it with us
Yes, at the train station there is an attended luggage area.
Just to clarify, there are two train stations in Pisa. While it is advertised that Pisa Centrale station has luggage storage, the closest station to the Duomo, Pisa S. Rossore, did not have a luggage storage office or luggage lockers when I went through there 3 years ago.