The substance, which is found in the digestive system of sperm whales, is valuable and used in perfume.
Ken Wilman from Morecambe said when Madge the dog "started poking at a rather large stone" he realised it was unusual.
He left the ambergris on the beach but "something triggered in my mind" and, after doing some research, he went back to get it, BBC News reported.
"When I picked it up and smelled it I put it back down again and I thought 'urgh'. It has a musky smell, but the more you smell it the nicer the smell becomes," Wilman said.
He is now waiting to get the three kg piece tested and said he had been offered 43,000 pounds for it by a French dealer.
"It's worth so much because of its particular properties. It's a very important base for perfumes and it's hard to find any artificial substitute for it," Andrew Kitchener, principal curator of vertebrates at the National Museum of Scotland, said.
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"Over time it becomes a much sweeter smell as it oxidises, but initially it doesn't smell very nice," Kitchener said.
Ambergris is a natural excrement thought to be used by the whale as a digestion aid and is expelled from its abdomen often while hundreds of kilometres away from land.
Initially, it is a soft, foul-smelling matter that floats on the ocean but through exposure to the sun and the salt water over years it turns into a smooth lump of compact rock which feels waxy and has a sweet smell.
It is still used in perfumes, although many perfume makers now use a synthetic version.