Green’s Dictionary of Slang

Lamington n.

[‘a soft felt hat with a curled brim and a dented crown, first worn at Homburg, once a fashionable health-resort’ (OED). Aus. use plays on SAusE lamington, a square of sponge cake coated in chocolate icing and desiccated coconut, ult. Baron Lamington (1860–1940), governor of Queensland]

1. (Aus.) a Homburg hat.

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Warwick Argus (Qld) 23 May 2/7: The Lamington hat and cane are established now in Queen-street, and the man without these necessaries is looked on as something in the light of a vandal.
[Aus]Brisbane Courier 7 Jan. 4/5: A boy named John Stenson picked up a Lamington hat on the river bank.
[Aus]Brisbane Courier (Qld) 11 Jan. 4/7: On the bunk near where the body was recovered an umbrella and a gray Lamington hat were found.
[Aus]Cairns Post (Qld) 15 June 2/5: [advert] At 9/6 is a Special Medium Leaf Bound Edge LAMINGTON STYLE HAT, suitable for elderly gentlemen, in Dark Brown only.
[Aus]Worker (Brisbane) 19 Dec. 7/3: Lord ‘Lammy’ and Labor. Lord Lamington, a Governor of Queensland in the late ’nineties, noted more than anything else for having bestowed his name on the Lamington (‘Lammy’) hat, but who is also remembered geographically in our Lamington Plateau.
[Aus]Baker Popular Dict. Aus. Sl.

2. (Aus.) the vagina [the dent supposedly imitates the female genitals; plus the pun on felt ? + hat n. (1)].

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[Aus]R.G. Barratt ‘Wellington’s On the Other Foot’ in What Do You Reckon (1997) [ebook] What if I [...] got two mates to throw beers over her and then I kicked her in the lamington?
[Aus]R.G. Barratt ‘Me Nude!’ in What Do You Reckon (1997) [ebook] [P]unters across Australia have seen your lamington.
[Aus]R.G. Barrett Rosa Marie’s Baby (2013) [ebook] Next thing he was looking into Sonia’s neatly trimmed lamington.