We have hiked from Compatsch, at the top of the gondola lift that comes up from Siusi (the big blue cabins) all the way to Mont Sëuc, which is where one catches the gondola down to Ortisei. (I do not know "Mezdi.") There is no need lifts in between although the one at Sonne can help you avoid an uphill trek at the very end. The hike takes us about 2 hours and is about 4 miles. Here is a write up I did on that very hike. Arriving at the top, make your way to the little village where you will find toilets, cafes, etc. (We always stop for a pre-hike cappuccino.)
When you are ready to depart Compatsch, head down the main road and turn left by the church to find the start of Trail #30, signed as the “Hans und Paula Steger Weg/Sentiero Hans & Paula Steger.” This section leads one gently through the lower meadow with views of Bullacia and some information stations about flora, fauna, and geology. Rejoining the road, turn left onto the path alongside the road, now Trail #3. Follow this until an intersection with Trail #6. Turn left here and follow signs to Baita Sanon Hütte (also sometimes called Malga Sanon), a great place for a break with good food, a WC, and great views. Continuing on, follow #6 toward Sporthotel Sonne (also signed as Sole), across rolling meadow always with a marvelous view. Sonne, a full-service hotel and restaurant, is another fine place for a break. Here you are less than 30 minutes on foot from Mont Sëuc, an uphill slog, in our opinion. We recommend hopping on the chairlift behind the Sporthotel Sonne (lift closed 12:30-13:30) and arriving at the top in style. A short walk brings you to a gorgeous viewpoint over the Alpe di Siusi to the mountains, Restaurant Mont Sëuc, and the ovovia to Ortisei. Descend to Ortisei and walk across the bridge to the center of the village, a short distance from the bus piazza.
This is about a 2-hour hike plus breaks, bus, and lifts, so five hours give-or-take as an outing, roundtrip from Ortisei. Alternatively, one can take Trail #9 or a combination of #9, #6, and #6A to ascend to the lift station at Mont Sëuc for a longer and slightly more strenuous hike. A point of confusion: not all maps call the top of the lift Ovovia Ortisei-Alpe di Siusi Mont Sëuc. Some of the less detailed maps just label the area as Piz.
The lift at Sonne and the ovovia are included in the Val Gardena Card.
Hiking boots and trekking sticks are optional. Much of this route is paved and the part that is not is easy to navigate.