Which is why the Celtic manager will not take any chances in the Scottish Cup tie against Peterhead on Sunday.
It's the one trophy Lennon has managed to get his hands on since becoming a boss.
He is determined to retain it, plus add the SPL championship – which they now lead – and the League Cup, in which they are just one step away from the final.
Lennon believes his players are up for the Treble challenge and said: "We want to win everything.
"We came very close last year, but they know they have to do better now.
"I think we've got a better squad. And we've still got Kris Commons to come back." The midfielder was a massive hit when he arrived in last January's transfer window.
Commons has struggled to recapture that form this season, and a handful of English clubs are monitoring the situation.
But the manager believes no one is looking to move out at this stage as they are all united in their ambition to bring trophies back to Parkhead.
"They have started something here, and I think they want to see it through," said Lennon.
"They are very highly motivated after last season, and they will not get a better feeling than the one that's around the club at the minute with the supporters and the connection they have got.
"So, unless we get an absolute knockout offer, and it is best for everyone involved, particularly the club, then we won't consider selling anybody."
Lennon is still looking to add another central defender and a striker, and 33-year-old West Ham front man Frederic Piquionne is the latest name to be linked.
But the Hoops may have to divert £2million to exercise their right to buy Fraser Forster from Newcastle as Spurs are reported to be ready to make a move for the 23-year-old.
And Aston Villa boss Alex McLeish could be set to test Celtic's resolve by making a £6m bid for South Korean playmaker Ki Sung-Yueng.
A bounce game against Hibs, arranged to give the likes of Emilio Izaguirre and Kelvin Wilson match fitness after injury, was cancelled due to the stormy weather yesterday but could go ahead today.