The Hoops have held top spot for much of the season but now find themselves four points behind Rangers, who have played two more games.
They then take on Rangers at Ibrox on Sunday in what could the defining moment of the season but Lennon has faith in his charges.
"We want to win the league and we want to win the Cup,” he said.
"We fell short in the League Cup Final but I don't think we're feeling the pressure.
"People talk about experience and sometimes it's handy to have.
"Every year is different and the pressure is still the same. Every game is a must-win. We've shown a real will to win allied with hunger and desire.
"We've also played good football under a lot of scrutiny.
"We've fallen short a couple of times but the players have learned from that."