After our stay in Lecce, we intend to travel north, probably to Umbria, preferably on Friday September 20. The Italian train website shows night trains from Lecce north to either Bologna or Rome Termini to be sold out. Is this likely correct, or is it possible that they just haven't opened up reservations yet? I see only one date on which I could purchase tickets. Do these seats really sell out 4 months in advance?
Without checking for myself, I will offer one comment. Are you getting the message -- No solution Found. Or you getting a sold out message? It is possible the schedule has not been posted. The next six months of schedules should be released around Jun 1 or later. I am guessing that is your problem.
"Sold out seats on Train XXX. Solution cannot be purchased."