In a game played in freezing conditions, the Gayfield Park pitch was rock hard and the SPL leaders struggled at times.
Lennon said after the 1-0 win: "It was a performance full of character.
"It was a horrible night. The pitch got worse as the game went on and you could see how difficult it was to play on. It became almost like an ice rink.
"I was worried about the safety of the players but they showed their professionalism tonight and great character. The pitch was definitely a leveller."
Adam Matthews' brilliant first-half strike was the difference between the two sides and Lennon was full of praise for his right-back.
The Northern Irishman said: "He's a great athlete, he's got great pace and we've been asking him to do more of that.
"He was far more productive in his offensive play on Saturday and again tonight. He was probably our best outlet and the goal was a real thing of beauty."
Arbroath felt a little aggrieved at not forcing the game into extra-time after having a 66th-minute goal by Steven Doris ruled out by referee Craig Charleston - apparently for a foul on Hoops keeper Fraser Forster.
Player-manager Paul Sheerin said: "I didn't see much wrong with the goalkeeper, I didn't see too much impeding. It didn't look like a foul, that's for sure."