Chiefly used in Australian English, the colloquial phrases like a lily on a dustbin, like a lily on a dirt-tin, and their variants, refer to something or somebody that is incongruous or conspicuous.

The earliest occurrences that I have found of the phrases like a lily on a dustbin, like a lily on a dirt-tin, and variants, are as follows, in chronological order:

1-: From The Ebony Beetle, by M. W. Wesson, a Tea Time Tale published in the Leicester Mercury (Leicester, Leicestershire, England) of Friday 10^th August 1934 [page 18, column 3]:

Roger was surprised to find things of so much beauty there. Cut glass, hand-painted vases, carvings in wood and ivory.
Roger came away greatly impressed, invigorated, thrilled by the beauty he had seen. Funny, he thought, finding things like that in such a dusty untidy little shop in a back alley . . . . Like finding a lily in a dustbin . . . .

2-: From Beauty Hints from M.P.’s, published in the Maryborough Chronicle (Maryborough, Queensland, Australia) of Monday 28^th June 1948 [No. 23,829, page 2, column 4]:

Wearing that exciting new shade of lipstick, stolen from the heart of a rose, fragrant with that delicate dew-petal face powder, the prospective M.P. will turn on great gobs of sex-appeal. Gooing and gurgling like a lily on a dustbin he’ll limp into the avid ears of the flapper Press the confidential secrets of his New Look.

3-: From A Dictionary of Slang and Unconventional English. Colloquialisms and Catch-phrases, Solecisms and Catachreses, Nicknames, Vulgarisms and such Americanisms as have been naturalized (New York: Macmillan Publishing Co., Inc. [1970]), by the New Zealand-born British lexicographer Eric Honeywood Partridge (1894-1979) [page 1391, column 2]:

shag on a rock, standing out—occ. sitting—like a; or…like a lily on a dirt-tin; or, rarely,… like a beer bottle on the Coliseum. These picturesque Australian similes, dating from, resp., ca. 1930, 1935, 1945, bear three distinct senses: Lonely, as in ‘He shot through and left me sitting like a shag on a rock’; conspicuous, as in ‘It stood out like a lily on a dirt-tin’; incongruous, as in ‘He was as out of place as a beer bottle on the Coliseum’.

4-: Book title: Lily on the Dustbin: Slang of Australian Women and Families (Penguin Books Australia Ltd., 1982), by the Australian author Nancy Keesing (1923-1993).

5-: From a review of Nancy Keesing’s Lily on the Dustbin: Slang of Australian Women and Families—review by Gerald Alfred Wilkes (1927-2020), published in The Sydney Morning Herald (Sydney, New South Wales, Australia) of Friday 24^th December 1982 [No. 45,237, page 19, column 2]:

Miss Keesing has set aside printed sources for material from conversation, family reminiscences, radio phone-ins and letters from correspondents, dedicating the book “To the Australian Folk.” This procedure shows how much more slang is in currency than gets written down. Although like a lily on a dirt-tin, implying incongruity, is recorded by Partridge as going back to 1935, I have never encountered it in print.

6-: From the column From the gallery, by Mike Seccombe, published in The Sydney Morning Herald (Sydney, New South Wales, Australia) of Wednesday 23^rd March 1988 [No. 46,876, page 4, column 5]:

After all the post election ¹ recriminations, even Mr Hawke was taciturn and stony-faced, but Mr Keating played on as if what happened in NSW last weekend was just a temporary setback.
He enriched our vocabulary, as he has done so often before. The Opposition, he said, were sitting back chortling over Saturday’s results in NSW as if they were “lilies on a dustbin”.
The phrase, according to his office, referred to someone trying to look flash, while sitting on something malodorous.

¹ The New South Wales Labor Party had been defeated in the elections to the 49^th Parliament of New South Wales, held on Saturday 19^th March 1988. Bob Hawke (1929-2019) was the Leader of the Australian Labor Party and Prime Minister of Australia, and Paul Keating (born 1944), of the Australian Labor Party, was the Treasurer of Australia.

7-: From How to Satisfy a Man Every Time . . . and Have Him Beg for More! (New York: Kensington Books, 1999), by the U.S. actress and author Naura Hayden (Norah Helene Hayden – 1930-2013) [Chapter 2, page 32]—the quotation is probably from Prattling on with Noelene Hogan (McMahons Point, N.S.W.: Margaret Gee, 1992), by Noelene Hogan:

When I was down in Australia in 1992 […], I read an excerpt in a magazine of a book by Noelene Hogan who was married to Paul Hogan ² and was now his ex-wife. […] But after reading part of Noelene’s book in the magazine, I can understand why he left. Noelene is very sweet, unassuming, pretty, but with zero self-esteem.
“Paul had a habit of not introducing me to people. I would stand there like a lily on a dirt bin and feel totally insignificant.”

² The Australian actor Paul Hogan (born 1939) is best known for his role as Michael ‘Crocodile’ Dundee in the Crocodile Dundee film series (1986-2001).