TORONTO (AP) _ Allied-Lyons PLC announced one of the biggest lawsuits in Canada's history today, saying it wants the Canadian equivalent of at least $3.6 billion in damages from Hiram Walker Resources Ltd. if Hiram Walker does not complete the sale of its liquor unit to Allied-Lyons.

The British company said it primarily wants a court ruling compelling Hiram Walker to complete the sale, together with monetary damages to compensate Allied-Lyons for the sale's delay and 1 billion Canadian dollars in punitive damages. A Canadian dollar is worth about 72 U.S. cents.

The amount of the damages sought related to the delay will continue to build until the sale is completed, and so far it totals 1.5 million Canadian dollars, said Jack Nusbaum, a lawyer with Willkie, Farr & Gallagher in New York, Allied-Lyon's outside counsel.

In the event the court does not order Hiram Walker to sell its liquor business to Allied-Lyons, then the British company will seek 4 billion Canadian dollars in damages plus the 1 billion Canadian dollars in punitive damages, Nusbaum said.

Sir Derrick Holden-Brown, Allied Lyons' chairman and chief executive, announced the lawsuit at a news conference in Toronto.

''While it is not in keeping with Allied's philosophy to conduct its business by litigation, it is wholly unreasonable to expect us to stand idly by while hostile attempts are made to frustrate our binding agreement to acquire the spirits and wine division of Hiram Walker,'' he said.

Allied-Lyons is seeking damages from Hiram Walker; Gulf Canada Corp., its new majority stockholder; Olympia & York Developments Ltd., Gulf Canada's parent; Paul and Albert Reichmann, who are members of the Reichmann family of Toronto that control Olympia & York and Gulf Canada; and certain Hiram Walker directors.

''We regret that we have been forced to take this step,'' Holden-Brown said. ''We are not accustomed to conducting our business by litigation. But enough is enough.''

The dispute began earlier this year when Hiram Walker, in a bid to thwart a takeover attempt by Gulf Canada, agreed to sell its liquor unit to Allied- Lyons for about $2 billion.

Hiram Walker's liquor group makes such well-known products as Canadian Club whisky, Ballantine's scotch, Courvoisier cognac and Kahlua liqueur.

But before the sale could occur, Gulf Canada succeeded in buying control of Hiram Walker. Gulf Canada then replaced the Hiram Walker board with its own nominees, and on May 22 Hiram Walker announced it had withdrawn from the proposed transaction with Allied-Lyons.