The ticket you hold requires a change in Lugano. You cannot continue on the EC 151 after the train has crossed the Swiss/Italian border, as your ticket is not valid for the EC 151 in Italy. In most cases, tickets that require a change of trains in Lugano are Saver tickets, and an alteration / exchange of Saver tickets is not possible (please check though with the SBB Contact Center by phone +41 51 225 78 56, available 24/7, waiting times may occur). If you stay on board the EC 151 with your ticket, the Italian railways ticket inspectors may inquire a hefty surcharge.
That said, the 4-minute change in Lugano is usually well doable; if it would not, it would not be offered as a connection. In the station of Lugano, there are ramps, and escalators on the platform for people with luggage.
There is another issue with this connection, that could make a change of trains in 4 minutes impossible: from my experience, as I work frequently as train conductor on the Eurocity train, the EC 151 is often arriving late from Germany. This means, it can be that the connection in Lugano is not possible as the EC151 is running so late, and, consequently, you would anyway have to take the next RE train from Lugano. In such a case, your ticket remains, of course, valid. Trains between Lugano and Milano Centrale do run frequently.
→ In order to make up the delay, the EC 151 is sometimes rerouted and not running via the station of Lucerne. In such a scenario, there is a replacement train at 12:18 that takes you from Lucerne to Arth-Goldau, where the EC 151 will stop and pick you up. This concept allows the EC 151 to be on time again at arrival in Lugano, to make the connection. If there is a huge delay, the connection might be impossible and you will have to take the next train from Lugano, as described above.
It sounds all confusing, but it isn’t. You won’t be the only couple taking the EC 151, followed by a change of trains in Lugano for Milan. It will be a smooth travel, just follow the crowd. Furthermore, all announcements will be made in English, too. We train conductors do speak English as well, as you can see by my response.
One last advice: I would suggest going to the Coop store in the station of Lucerne and buying a pick-nick, which you can enjoy on board the Eurocity while the train crosses the Alps at high speed through the world’s longest railway tunnel. The food in the EC 151 restaurant car is unfortunately not that delicious, although the restaurant is operated by the Italians; however, the espresso coffee is excellent.