Celtic captain Callum McGregor pointed out “it’s in our hands” after Sunday’s “huge win” over their city rivals.
Only defeat by Motherwell on Wednesday, combined with a Hearts win, will prevent a final-day showdown.
Nevertheless O’Neill believes Celtic still have “two mountains to climb” if he is to lead them to the Scottish title for a fourth time – and his first in 22 years.
“I’ve never been confident,” the 74-year-old Northern Irishman said. “People have said to me about momentum and momentum can get shifted at any given moment.
“We have to win because I would expect Hearts to win. We’ve a really difficult match at Motherwell, but I think the run that we’re on gives us confidence to compete.”
O’Neill would not be drawn on whether it would be his final Old Firm derby when asked if a league and cup double might persuade him to stay on at Celtic.
However, Lennon thinks giving the veteran a winning send-off will be another motivating factor for the players.
Hearts are unbeaten against Celtic this season, winning two of the three meetings, but Motherwell midfielder Andy Halliday also pointed to the O’Neill factor as potentially crucial.
“Of Celtic’s January signings, none are in the starting line-up,” the former Hearts and Rangers player said. “So what he’s done is make all the players Celtic already had at their disposal better.
“Celtic are on a five-game winning run. You talk about mentality and playing your best level at the right time and Celtic have hit theirs now.
“But Hearts, for 30 weeks in a row now, are just finding ways to win, so it’s going to be a very interesting finish.
“We were salivating for these post-split fixtures and they’ve been everything we hoped for. I don’t think that’s going to change.”
