The Bhoys host Rangers at Parkhead one point behind their rivals in the SPL table, having won eight straight games to reduce a 15-point deficit.
It gives Celtic a fighting chance of wrestling the SPL trophy from Ibrox for the first time in four years.
“I want to win things and there is a real determination in the camp to start winning trophies this season,” Lennon said.
“But there is still a lot of football to go.”
Lennon is delighted with his team’s character after the 2-1 win over Kilmarnock sent his side into the derby in rude health.
“We are improving all the time and the players have a good mentality,” Lennon said.
“Ki Sung-yueng has been very good since he recovered from a virus, Scott Brown got stronger as the game went on and Cha Du-ri has been fantastic in the last three or four games.
“Any slip-up could have cost us and the only blip we have had since the Hearts defeat (in October) is the 0-0 game at home against Hibs, when we didn’t play as well as we could have done.”