Balakrishnan tweeted that they were celebrating Trump's birthday "a bit early."
He did not respond to BuzzFeed News' request for details on the surprise birthday celebration and the type of cake.
Other dishes on the menu included lobster bisque and beef tenderloin.
"As you know, we've got a very interesting meeting tomorrow," Trump told Lee during the meeting. "We've got a very interesting meeting in particular tomorrow, and I just think it's going to work out very nicely."
"We do appreciate your hospitality, your professionalism, and your friendship," Trump added.