TMac,
I haven’t found any mention of Tillie/Lees in connection with Green Meadow. The closest I could place Lees was right next door at Apawamis in 1920, where he was making some substantial changes to the greens at the 4th, 5th, 8th, and the 18th.
I’ve also come across a 1928 article mentioning that “…a group of young college and professional men of the University Golf Club”….. bought the old Turnpike Golf and Country Club, near Great Neck Long Island and that new ‘links’ were “….laid out and developed last spring under the direction of Devereux Emmet, golf architect”.
I don't know if this place is something 'new' or it's something that's already known, but by a different name.
I also found a 1926 article that places Emmet in Oswego, NY, planning changes to nearly all of their greens (and possibly some re-routing) for the purpose of modernizing the course. OCC was started in 1897 and Tillinghast did some re-modeling of this course in 1915.
edit: Still no mention of Lees, but I did find that Green Meadow was successively known as Ferncrest, Hasty Brook, Willows and Harrison
Country Clubs before becoming Willow Ridge.