Thomas Robert Smith - Poetica Erotica: A Collection of Rare and Curious Amatory Verse (1921)
Open Library direct link (volume one)
Open Library direct link (volume two)
Open Library direct link (volume three - supplementary)
Open Library main page
This isn't exactly what you might first suspect. The Latin title, the "subscribers only" notice, the dedication to Mencken & Nathan - all might suggest a more explicit collection of under-the-counter literature than what is actually presented. The "amatory" in the title might indicate where it's really going as well as included authors such as Donne, Marlow, Beaumont & Fletcher, Behn, Villon, Herrick, Ovid and so on. It's basically love poetry leaning more towards the flesh than the spirit.
Mabel Norman owned a copy (Anderson's Twilight of the Idols, note p201).
Thomas Robert Smith (1880-1942) was an editor at The Century from 1914 to 1920. (This conflicts with Wikipedia and some other sources but it's in the NYT obit. He was definitely there from 1919-1920. Online scans of the magazine are poorly indexed so it's hard to check.). In 1921 he became editor at Boni & Liveright who published this book that year. Nathan says he and Mencken first met Sinclair Lewis at Smith's apartment (Sinclair Lewis Remembered). Bennett Cerf described Smith as "very erudite, round-faced, gray-haired cherubic man who wore a pince-nez with a black ribbon". (At Random p31)