I’ve hiked the LT twice - both times in September. (which BTW is my favorite month to hike in New England: no bug, Fall foliage & perfect hiking temps)
Nighttime temps can vary considerably over the course of the month - anywhere from the 70’s to below freezing. I think you will be fine with the 30* bag - just make sure to put on extra clothes on the frigid nights (which should be far and few between).
Also, there a number of warming huts along the trail at many of the ski areas where you could stay if its exceptionally cold. Bromley, Sugarbush, Mad River Gled, & Smuggler’s notch all have warming huts that hikers can use on the summits of their mountains. Besides these huts, the GMC has a bunch of ‘lodges’& enclosed cabins along the trail as well (for a small fee). So… you have a bunch of options in case you run into unseasonably cold temps & your 30* bag should be just fine otherwise.
Happpy Trails!
freebird