The woman replied: "Hope you get caught one day, would love to see that. I know we're a minority and really don't give a sh*t because that has no relevance. Enjoy the heart disease."
Vegans across social media shared the post and flooded the Facebook page of the hotel where Lambert worked with one star reviews.
The hotel initially suspended the chef after insisting his comments were only made "in a heated moment" and that "this practice has never taken place."
But the rage from the vegan community only intensified, with many calling on customers to boycott the hotel.
Doreen McCluskey wrote: "The chef at this hotel prides himself on sneaking pork bits in the food of people who can't eat it. He thinks that it's very funny. I suggest that you eat elsewhere unless you want to be the butt of the joke and be sick, after paying good money for your food."
And Abigail Elizabeth Suter wrote: "People have a right to know what goes into their food. If I asked for a vegan dish and was told that is what I'd get then I'd expect a vegan dish. Not something where the chef has been sneaking animal products into it for a laugh."
The chef's suspension was then escalated to a termination. The hotel chain released a statement saying they had investigated the accusations and while no evidence to the claims was found, due to Lambert's comments regarding "specific dietary requirements" the company has decided to terminate his contract.
According to the Daily Mail, Lambert's Instagram account profile described him as a "carnivore" and told people to "stop being so sensitive".
The account, along with his Twitter and Facebook, has been deleted.
Lambert has since spoken out about the incident saying: "I have been a chef for nine years. I have never in this time done anything like feeding a vegan animal products or slipped in contaminated food.
"My job has always been my passion and something I have always taken very seriously. It was a stupid comment said out of anger.
"For the record I have no issue with vegans."