He also claimed that seat reservations were not valid on the train at that time because there had been an announcement that seat reservations were no longer valid because the train was crowded.
MailOnline has tried to contact Lees to verify the claims she made on Facebook.
MailOnline also contacted Virgin East Coast to verify the circumstances around Lee's ticket reservation.
A spokeswoman would not comment on the specific case but said customers are entitled to their reserved seat, an alternative or a refund.
Lee claims she took a friend for support on the three hour journey but said both were left to stand on the busy train for more than an hour before she managed to find another seat.
The mother-of-one says she suffered nerve damage and crippling groin pain following an operation, which left her unable to work.
Lee shared her story on Facebook.
She wrote: "Meet these gentlemen. Travelling from London Kings Cross on the 18:03 to Skipton.
"Charming fellows took reserved seats from Rach & I. As a disabled passenger, I stated why I needed my reserve seat. They didn't budge.
"I'm sure their wives and mothers would be proud of them."
Lee said the two men spent most of the journey "talking about luxury holidays in the Caribbean and Dubai" before eventually getting off at Leeds.
Speaking on Lee's behalf, her friend Kath Sansom said: "Cat told them they were in her reserved seats and the men totally ignored her and kept staring at their phones.
"The aisles were rammed packed so they were unable to push past everybody to try to find a guard. She was in pain and needed her friend there for support.
"Cat feels angry that people think they can do as they please with no consideration for others. The seats are reserved. End of. I just hope it sends a message to others not to do this to people."
A spokeswoman for Virgin East Coast said: "If a customer's reserved seat isn't available our on-board team will either ask people to move from the reserved seat or find an alternative.
"On our east coast services we also have our seat guarantee - so if we can't find you a seat when you've reserved one, you'll get a full refund for that journey."