a VirtualTourist member from Fort Lauderdale
What is the best way to travel between Lecce and Naples?
Train takes 5-6 hours, and may well be your best option.
www.trenitalia.com/en/index.html will give you train times, details and fares in English. At least one train only has one change, others have more than one.
One-way fare is 42 euro.
You can also get a bus, operated by Micolis. Timetable linked on this page:
Takes around 6+ hours, costs 28 euro one-way.