Recommended order for visiting Lucca & Pisa on our way to Cinque Terre?

Visit Lucca on your way to Cinque Terre and Pisa on your way to Rome.

From Florence you have to go through Lucca to get to either Pisa or 5 Terre. So, Lucca first. I took trains from Lucca to 5 Terre through Viareggio and La Spezia without ever going to Pisa. As above, see Pisa coming back if you are headed south.

Thanks gerri/Gordon. Our plan was to visit both cities (Lucca/CT) on the way up. Admittedly, I took a risk and pre-booked a train ticket from La Spezia to Roma Termini to save some money on our way back that aren't refundable so it kind of forces our hand :/ We'll plan on Florence -> Lucca -> Pisa -> CT

Side note, I'm wondering if it's legal to board a train at a later station to possibly use part of the pre-booked tickets? In any case, I won't be too hurt if we end up abandoning the train tickets.

Popping in to say that I visited Pisa last year in July in the afternoon and it really wasn’t that bad. Sure, it was crowded, but nothing unmanageable. I recommend doing the following to manage waiting. First, go online and buy the five euro ticket to the baptistery. This also gets you a fast pass into the cathedral. Also if you’re interested in climbing the tower those tickets will get you a fast pass into the cathedral as well. Yes, the cathedral is free but it will only accommodate so many people at one time and you have to go to the very end of the square to get a time stamped entry, which may be a long time later. Spending five euro per person avoids all of the finding the ticket booth and waiting around parts. Plus the baptistery was very interesting and I enjoyed climbing to the top of it for an excellent view of the tower. I really enjoyed Pisa despite thinking that it was going to be a tourist trap. I only went there because my kids wanted to go and I actually ended up really enjoying it a lot.

Few if any trains from Florence to Pisa or Cinque Terre travel via Lucca, as Lucca is on a different rail line than Pisa. However, the fact that it's easier to catch a train to Cinque Terre from Pisa actually validates your decision to visit Lucca first. Depending on what trains you plan to take, you may be able to get off and back on at the S. Rossore station, which is a relatively short but not well marked walk to/from the Field of Miracles. Regional and Regional Veloce trains will likely stop at S. Rossore whereas Freccia and Intercity trains will not.

Not sure I understand your question about boarding at another stop, but generally you can board at a later station on the route for which you purchased a ticket. For example, if you bought a Pisa Centrale to La Spezia Centrale regional train ticket you could board at Pisa S. Rossore. For a pre-booked (online purchase?) ticket, travel would need to occur within the pre-validated time limit.

Someone on this forum actually suggested (over a year ago) that it was best to go to Lucca first, because by the time you get to Pisa most of the bus tours will have departed. However, if you want to go inside any of the buildings there, you'll need to check their hours and also investigate whether you can buy entry tickets in advance or may have to suffer a line.

The Leaning Tower of Pisa seems to be something just about everyone feels he/she has to see. I think most folks (well, most adults) who do both like Lucca better, so I recommend an early start so you have a reasonable amount of time in Lucca.

Thanks Frank and Acraven. This makes me feel better about a plan to go to Lucca first followed by Pisa -- but we'll stay flexible just in case and get the train tickets when we're there.

Because I was feeling guilty about purchasing the Riomaggiore -> Rome in advance given everyone's suggestions to go to Pisa on the way back... I was wondering if I could book a separate Riomaggiore -> Pisa ticket earlier in the day of my return trip to stop in Pisa and then meet back with my original booked train at a later station (when it gets to Pisa). I'm not sure if in Italy/Europe it's frowned upon to not board at the ticketed departure station and instead go on at a later station for the trains route.

I found these threads but not sure how much validity they still hold:

https://www.tripadvisor.com/ShowTopic-g187768-i20-k5205728-MiniTrainticketboardingatdifferentstation-Italy.html
https://community.ricksteves.com/travel-forum/transportation/italy-regional-train-ticket-can-you-board-at-a-later-staion

Under most circumstances I think there's nothing wrong with boarding your booked train at a later stop--though there may be someone sitting in your seat that you'll need to evict (politely, because they will be justifiably disappointed). Just within the last few weeks I read there can be issues with delayed boarding in the UK, because the passenger may have gotten a deal on a cheap Advance ticket for the entire trip when a similarly inexpensive ticket would not have been available for the shorter segment actually traveled. But there are some anomalies with UK rail fares that I suspect don't exist in most other countries. The UK has lots of different rail companies, which seems to complicate things.