train from Lucca to Cortona

Both trains - Lucca to Florence and Florence to Cortona - are regional trains and you will likely get 2 tickets, 1 for each leg. Regional trains give you the flexibiity to purchase open tickets good for any time - no reservations needed or possible - so you could spend some time in Florence if you wanted. Change in Florence is easy. Walk to front of station and look at board to determine from which track your Cortona train departs. Depending on change time, it might not yet be posted when you arrive. If you have 2 tickets, be sure to validate the correct one at each station.