Caretaker manager Lennon confirmed on Monday he had already handed major shareholder Dermot Desmond and chief executive Peter Lawwell the names of those he believes should be sold at the end of the season.
If the former Parkhead captain's behaviour during Saturday's shock Scottish Cup semi-final defeat is anything to go by, Landry NGuemo, Marc-Antoine Fortune and Georgios Samaras may well feature on that blacklist.
NGuemo was hauled of before half-time at Hampden, while Lennon singled out forwards Fortune and Samaras for criticism in what was a scathing post-match press conference.
Whether that trio enjoy a stay of execution in Tuesday night's SPL game against Motherwell remains to be seen.
But those who do feature at Parkhead will be left in no doubt what Lennon expects from now until the summer.
"Ultimately, we have to qualify for the Champions League," said Lennon, who questioned whether his under-fire squad has what it takes to hold on to second place in the SPL.
"I did come out and say what I felt on Saturday; now I want them to prove me wrong.
"They're playing for their futures here.
"Do they want to stay at this club? Well, they've got six games to prove it."
Lennon hopes "pride" will be the minimum his players show on Tuesday.
"We're probably stripped down to the bare bones in terms of that," he said.
"It's a powerful thing though, professional pride, pride in yourself as a man and pride in your performance."
Lennon, who was on the wrong end of similar shocks during his playing career, warned his players Saturday's result would haunt them for some time.
"Don't forget, because you won't be allowed to forget it anyway; it'll linger for a while," he said. "It had better be hurting the players because, if it doesn't, I don't know what will."
Star striker Robbie Keane confirmed the atmosphere in training had been suitably "sombre".
He added: "Lenny was saying to the lads there it's important that we pick ourselves back up because, at the end of the day, we have another game on Tuesday."
Celtic's week went from bad to worse on Monday when the Scottish Football Association handed striker Morten Rasmussen a one-match ban after finding him guilty of elbowing Kilmarnock's Fraser Wright in last month's cup quarter-final at Rugby Park.
And Motherwell midfielder Steve Jennings aims to pile on more misery.
"If I was a Celtic fan I would be disappointed at the way my season has gone," he said. "We've got to go there with our game plan and if that upsets a few people, then so be it.
"We can just go there and play our game and hopefully do what we have been doing to teams in the first half recently."