The Hoops surrendered the advantage in the SPL title race to their Old Firm rivals by losing to Inverness on Wednesday night.
However, goals from Scott Brown and Kris Commons against Kilmarnock at Rugby Park yesterday took them back to within one point of the champions, who beat Hearts 4-0 at Ibrox on Saturday after beating Motherwell 5-0 at Fir Park the previous week.
Celtic’s goal difference superiority has consequently been cut to three and Lennon is looking for United to do him a favour against Rangers, 24 hours before the Parkhead outfit make the trip to Tynecastle to face Hearts.
“We have two games to go and anything can happen,” said Lennon.
“What we are looking for is somebody to compete and give Rangers a game.
“There has not been much evidence of that in their previous two games.
“Even if we had drawn the game against Inverness on Wednesday night, I’m not sure goal difference would have made a difference, looking at the two games that Rangers have had.
“Dundee United have something to play for now (a European place).
“The results went for them at the weekend and they are looking for a result on Tuesday and we will be looking for a result on Wednesday.
“I didn’t see the team Hearts put out, we were training at the time but listen, every team has their own agenda,” added Lennon.
“I’m not going to cast aspersions at other clubs.
“I didn’t see the (Rangers) game yesterday so I’m not going to sit here and criticise anyone’s performance.”
Lennon acknowledged the importance of his skipper Brown putting Celtic ahead in first-half injury time with a close-range header, after Gary Hooper and Commons both had the ball in the Killie net only to be flagged for offside.
“We had two goals disallowed, I’m not sure why,” said Lennon.
“I’m getting conflicting stories, I was told one was for a handball and then I was told both were offside.
“I will need to look at that. I thought we would score in the game, it was just a matter of when, but it was a great time to score.
“Scott is the captain and he came up trumps again.”
Lennon claimed that pound-for-pound there has not been a better signing this season than Commons, who arrived at Parkhead from Derby in January.
The Scotland midfielder’s wonderful drive from 25 yards in the 68th minute took his overall total for the season to 28, 13 of them for Celtic.
“I wouldn’t have thought (there has been a better buy), not for £300,000.
“Mind you, Emilio Izaguirre at half a million/£600,000, has been a fantastic bit of business as was Beram Kayal, at €1.2m.
“So we have been lucky in that respect, the players we have brought in this season have been magnificent.
“Kris is coming to the peak of his career.
“You almost get disappointed when he lashes a couple over the bar, he’s that good.
“You can look at four or five of his goals for goal of the season.
“He has been tremendous, he has a tremendous work rate and he is always likely to pop up with a goal.”
Lennon also revealed he took Emilio Izaguirre off in the second half purely as a precautionary measure.
KILMARNOCK: Bell, Clancy, Hay, Sissoko (Pursehouse 57), Agard, Bryson, Eremenko, Dayton (Fisher 77), Pascali, Silva (Taouil 65), Kelly. CELTIC: Forster, Izaguirre (Mulgrew 70), Majstorovic, Wilson, Rogne, Brown, Commons, Ki, Forrest (Maloney 65), Hooper (McCourt 87), Murphy.
Ref: William Collum (Scotland).