Green’s Dictionary of Slang

lily adj.

[SE lily, i.e. white in colour]

SE in slang uses

In compounds

lily shallow (n.)

a low-crowned white hat, esp. as worn by a coachman.

[UK]Sporting Mag. Mar. 280/1: Say nothing; leave all to me: you shall slip on my lily shallow and upper toggery.
[UK]‘An Amateur’ Real Life in London I 102: A green coat, white waistcoat, buckskin breeches, and boots, over which a pair of leggings appeared, which extended below the calf of the leg and half up the thigh, surmounted with a Lily Shallow.
[UK] ‘Larry Cafooslem’ in Laughing Songster 159: And with a lily shallow, / I sported a tidy tile.
lily tile (n.)

a white hat.

[UK]‘Knowing Bill’ in Rake’s Budget in Spedding & Watt (eds) Bawdy Songbooks (2011) III 87: On Sundays too, my rummy lads, / I comes it strong and flash; / Vith my lily tile and Benjamin.