You are fine to travel within Switzerland without a reservation. In Italy you need a reservation on the fast trains. I guess that you have to make the reservations for the trains in Italy on the national Italian Railway site, but there are others in the community who are experts on booking Italian trains.

No, canNOT do that on site of TrenItalia-as has been told here more as a few times. CAN do-a bit sneeky/roundabout, via oebb.at - READ explanation so often stated here- or simply (this ages old trick seems to baffle todays youth) pop INto the counter after arr. in Lausanne and let them do it for you. Just dont rush right out of that station-it is quite beautiful to also take a little longer look @!

You can easily find out for yourself whether this is possible. Here is an example of the options on the travel date 1 June.

You can do this connection without a mandatory reservation, but then you are on the road for a good 10 hours.

planners :  SBB, DB BAHN en OEBB.

Please note, that you can take the EC37 without a reservation till Domodossola (border to italy), where also the train staff changes, but to be 100% with the rules, you need a reservation from Brig (last station in Switzerland), if you are not continuing you trip back to Switzerland. From Domodossola there is a small railway that brings you to Locarno (Switzerland), from there you can get back to Italy and Milan with regional express. 

Alternative: You can also change in Brig to a Regional Express to Domodossola. From Domodossola a Regional Express to Milano Centrale.

From Milano Centrale a Regional Express to Verona P.N. and from Verona a Regionale Veloce to Venice S. Lucia. 

P.S. The reservation for the EC 37 from Lausanne 08:18 to Venice 14:42 costs 11€ in 2nd class. You can book the reservation without booking fee via Austrian ÖBB (tickets.oebb.at - one way ticket - discount Interrail/Eurail Global Pass). 

Hi Sven, thank you for the timetable. How did you find the timetable? We want to travel on the 17th June. Do you know how we can make reservations?

If you mean the reservation for the direct train:

The reservation for the EC 37 from Lausanne 08:18 to Venice 14:42 costs 11€ in 2nd class. You can book the reservation without booking fee via Austrian ÖBB (tickets.oebb.at - one way ticket - discount Interrail/Eurail Global Pass). 

For long distance trains in Switzerland you have only optional reservation, but nobody reserve seats. 

Hi Angelo, thank you for your answer. I will check out the Austrian oebb website

This timetable comes from the Swiss Railways ( SBB / CFF ) .
You can also use these from DB BAHN, and OEBB.

@Angelo already gave the answer how to make the reservation.

There is also a very clear explanation made by @seewulf how to make reservations. Go to his profile, and search for the topic "How to make reservations"

bahn.com sbb.ch or trenitalia.com

How do I use our Eurail/Interrail passes when booking online through these websites? For example I looked at sbb.ch and there was no option to enter the passes

Depends from website to website

Sometimes you just select seat only (reservation) on other websites you find somewhere hidden the option to add Interrail or Eurail as Discount.