https://web.archive.org/web/20160102141 ... rc93sw.jpg shows Almshouse Station just compass SE of the Tewksbury Junction wye. The almshouse had been repurposed and renamed as the hospital, but maps weren't/aren't always accurate. A bit further east, flows not the Shawsheen, but the Shawshine.
As far as coaling service, most of Commonwealth's state hospitals did have that. 2 exceptions that come readily to recall would be Worcester and Rutland State Hospitals, but only because their elevations were far higher than nearby rail lines, so drayage would have been the final delivery. The Industrial School in Lancaster also had drayage, but only because it was a distance from the WN&P.
Ronald Dale Karr's The Rail Lines of Southern New England: A Handbook of Railroad History, 1995, shows passenger service between Wamesit and Lawrence ending in 1924 and abandonment for the Tewksbury State Hospital stretch of track in 1926 (p. 21).