However, Lennon feels their second comeback win at Parkhead in five days has boosted his chances.
Goals in the last 10 minutes from Marc-Antoine Fortune and substitute Morten Rasmussen earned Celtic a 3-2 victory over Hibernian on Saturday - their fourth consecutive win in the Scottish Premier League since Lennon replaced Tony Mowbray.
Mowbray never achieved such a consistent run and Lennon feels their late win, which followed a battling victory over Motherwell, was an encouraging sign that the spirit is returning following the shock Scottish Cup defeat by Ross County.
But he realises Celtic have another big test of their resolve next weekend when they face Dundee United at Tannadice.
Lennon claimed on Friday that Celtic could still win the league but, with Rangers moving to within a point of the title with victory over Hearts, pride is now the main motivation for the players.
But the former Celtic skipper is also desperate to keep his job and believes the latest win is some evidence he can do so.
"Yes, why not?" he said. "I've had one blip, well a big blip, and I accepted that and the players accepted that.
"That was a big win. That's four wins in a row, which we haven't done for a long time in the SPL so I'm really proud of them.
"My worry is, we have won two home games. can we replicate that away from home?
"Dundee United is a huge game. We have talked about turning points a lot this season.
"My worry is that they put on a performance like that and next week it's flat again.
"So I have got to be really wary of that against a very well organised, hard-to-beat Dundee United side.
"Can we replicate that character, that consistency, that quality at the right times, that never-say-die attitude, get the crowd on our side?"
Lennon was pleased with most aspects of Celtic's play but admitted they "don't do clean sheets" at the moment.
Robbie Keane slotted home a fourth-minute opener but Derek Riordan fired in from 20 yards moments later and Anthony Stokes gave Hibs the lead from the spot early in the second half after Josh Thompson had caught the Irishman.
But Lennon hailed his side's character to put Hibs under sustained pressure before the late turnaround.
That character is evident in the manager, whose touchline demeanour is almost the exact opposite from forlorn predecessor Mowbray.
The former Northern Ireland midfielder is even more animated than mentor Martin O'Neill and sprinted 30 yards to celebrate with Rasmussen after the Dane diverted home Fortune's 87th-minute cross.
Lennon, who saw Darren O'Dea limp off with an ankle injury, said: "I have lost weight because I'm not eating. I don't have the time. It consumes you, your whole mentality. You are thinking about it non-stop, but it's brilliant.
"Regardless of where I go in management, if I'm lucky enough to get a job, I will take that same passion and love for the game wherever I go.
"But I'm really enjoying my time here and I just want to get the best for the club in the next few weeks."
Hibs manager John Hughes felt his side sat back too much after taking the lead.
Hughes was considering adopting a more defensive approach after his side lost 4-1 at Hamilton seven days earlier but they were just as positive.
"I'm always an expansive coach," he said. "I come and have a go, I want people to express themselves and when I have got guys like Riordan, Stokes and (Colin) Nish on the pitch and Benji (Abdessalam Benjelloun) on the bench, they have always got goals in them.
"I just hope we don't go out in the final part of the season on a dip.
"We will just keep going out there and battering on and keep believing in each other."