Do I need reservation to travel from Milan to Lucerne if it is not by the Eurostar? I am unable to reserve if I for the train leaving at 12.20 and going via Monza, Chiasso and reaching Luzerne. Is it ok if I use the 4 day family pass?
All trains in Italy except Regional require a reservation so you need to make a reservation. I do not know the terms or restrictions of a family pass so I cannot say if it is OK or not. Is the pass for both Italy and Switzerland?
Which website are you using to see this run? I can't find it. I do see Regionale trains from Milan to Monza and Chiasso. But most of these trains depart from Milano-Porta Garibaldi and not Milano Centrale. I see these trains on www.trenitalia.com. From Chiasso to Lucerne, I have been looking on the Swiss website www.rail.ch. All runs seem to want to get you on an EC train for the segment up to Arth-Goldau. But, I'm betting you could take local regionale trains along the same tracks and do the same thing. What's a family pass?
I'm afraid I can't help with the pass you have - I've never heard of it. I can't find the train you mention. Where did you find it? Are you referring to a stopping train from Mi.Garibaldi? It takes a while to reach Luzern anyway, I wouldn't spend all day dawdling getting there...
The timetables on the German Rail site show this route: Leave Milano Porta Garibaldi (not Milano Centrale) at 12:38 (not 12:20), connect in Chiasso and Arth-Goldau, and arrive in Luzern at 16:41. The train from Milano Porta Garibaldi to Chiasso stops in Monza. Is this the one you mean? Like the other posters, I don't know what you mean by a family pass. Are you referring to the Swiss Family Card?
The Swiss rail site shows that route, departing Milano Centrale at 12:20, with changes at Monza, Chiasso, and Arth-Goldau. You have to put in Milano Centrale rather than milano to see it. The two segments in Italy are regional trains with no reservations. From Chiasso to Arth-Goldau you are on an IV Tilting train with reservations possible but not required. If you buy your tickets at the station, you can show your pass and ask how much of the route it covers. A Swiss Family Card, for example, will take children for free from Chiasso to Luzern, but has no effect in Italy.