The trail that climbs from Lago Combal up to Arp Vieille Superiore, then to Lago Checrouit and Rifugio Maison Vieille was free of snow and in very good conditions. Most of the huts/refugees from the ski area are open and serve meals or drinks. One or two bridges were also installed where the path crossed some small streams.
If you go from Lago Combal to Maison Vieille, just before Maison Vieille there is a very dusty path that can get muddy and slippery in bad weather.
In the Val Veny there is a free shuttle bus from the Courmayeur central bus station up to La Visaille (~40-50min walk from Lago Combal). You can find the full timetable on the operator’s website and in this PDF.
If you are doing the TMB towards Courmayeur and feel pretty tired, I strongly suggest taking the cable from Maison Vieille to Courmayeur (one chairlift and one gondola – 15€ for both), as the trail is very steep and mostly on the ski pistes.