In Australian English, Lady Blamey designates an improvised drinking glass made by slicing the top off a bottle.

The earliest occurrences of the term that I have found are from Smith’s Weekly (Sydney, New South Wales) of Saturday 13^th September 1941:

Mine’s a Lady Blamey!
Diggers New Beer Pot

Mrs. Macquarie’s ghost will have to be on the alert. Up till now, Mrs. Macquarie’s chair ¹ has been the most famous individual article in Australian feminine history.
Unless somebody tells General Sir Thomas Blamey ² to stop making the troops drink out of cut-down beer bottles, an article, satirically called after Lady Blamey ³, is going to eclipse the famous chair.
Returning troops say that “a Lady Blamey” is already known throughout the length and breadth of Palestine.
Troops say that an order was issued by General Blamey to the effect that, as Australian troops were able to buy too much beer in their canteens, he directed that the beer bottles be cut in halves, and the lower half used as a measurement and a glass.
Deposit On Glass
Digger gets one of these filled with beer for 10½d after depositing 4½d on the “glass”!
Returned men say they gave these rough beer pots the name “Lady Blamey” because the Australian Government didn’t authorise their presence in the Middle East any more than it did Lady Blamey’s.
While on the job “Smith’s” suggests that there should be a thousand ways of economising in the A.I.F. ⁴ without making troops drink out of cut-down beer bottles.

A Lady Blamey

¹ Mrs. Macquarie’s Chair is an exposed sandstone rock cut into the shape of a bench, on a peninsula in Sydney Harbour; it was hand-carved by convicts in 1810 for Elizabeth Macquarie, the wife of Major-General Lachlan Macquarie (1761-1824), Governor of New South Wales from 1809 to 1821.
² Thomas Blamey (1884-1951) was an Australian army officer. On Wednesday 23^rd April 1941, Blamey, who had commanded I Corps, an Australian Army corps based in the Mediterranean and Middle East Theatre, was appointed deputy commander-in-chief of the British Forces in the Middle East.
³ Olga Ora Blamey (née Farnsworth – 1905-1967) was Thomas Blamey’s second wife.
⁴ AIF is short for Australian Imperial Force.

However, the origin of the term is different according to the text containing the second-earliest occurrence that I have found—this text is Colorful drama in the pageantry of Melbourne, our military capital, by Alice Jackson, published in The Australian Women’s Weekly (Sydney, New South Wales) of Saturday 23^rd May 1942:

One friend of mine, an A.I.F. officer who’d been through the campaigns in Libya, Greece, and Crete, and had a long spell in hospital, told me:
“Lady Blamey was a perfect godsend to the sick soldiers. She used to visit us regularly, bring comforts, and write letters for those too sick to write their own. You can’t imagine what a joy it was for the men to have a talk with her.
“She was practical, too,” he said, “with a true Australian flair for improvisation. They were always short of glasses in the canteens, and she hit on the idea of cutting down empty beer-bottles. They always use them now, and the boys have christened them ‘Lady Blameys.’”

A soldier explained how he made Lady Blameys in a letter published in The Australian Women’s Weekly (Sydney, New South Wales) of Saturday 15^th April 1944:

Pte. C. Taylor to his sister, Mrs. Edith Lees, 10 Second St., Ashbury, N.S.W.:
“We have been making Lady Blameys. In other words, cutting down bottles to make glasses for our beer.
“You tie a cord on to the tentpole, wind the cord round the bottle just down from the neck, and while one joker holds the end of the cord the other slides the bottle up and down.
“When the bottle gets hot we dip it in a bucket of water, and off comes the neck as clean as a whistle.”

In The Courier-Mail (Brisbane, Queensland) of Saturday 13^th December 1947, K. J. Kavanagh, the Canberra correspondent for that newspaper, wrote that he had seen Lady Blameys at the Australian War Memorial, Canberra, Australian Capital Territory:

The collection for 1939-45 […] includes six “Lady Blamey’s.”
To prevent any thought that General Blamey might have been a polygamist, I hasten to explain that these are beer bottles cut down to provide drinking vessels.
The idea was first adopted by the A.I.F. in the Middle East.
Why the name? I asked the director. His reply was that the idea had originated with Lady Blarney. Some ex-soldiers may have heard other versions.
Whatever the reason, “Lady Blameys” served a very useful purpose. A surplus of beer bottles was used to solve the problem of a shortage of glasses.