The Parkhead club's traditional rivals re-emerged in the Third Division at the start of the season after their descent into administration and liquidation.
Without the usual championship challenge from Ibrox, Celtic have coasted through the league campaign with the occasional bump and are 15 points clear of Motherwell with five games remaining.
Lennon's side, who also reached the last-16 of the Champions League, are likely to clinch the title when they host Inverness in the first game of the post-split fixtures, and might even have claimed the trophy before then if the Steelmen slip up at Dundee United two days earlier.
Speaking in Glasgow ahead of Celtic's William Hill Scottish Cup semi-final clash with Dundee United on Sunday, Vennegoor of Hesselink, who won two SPL titles, a Scottish Cup and a League Cup in his three years at Parkhead between 2006 and 2009, spoke about his former team-mate Lennon's desire to win, regardless of circumstances.
"If you look how he (Lennon) did in the Champions League and in the league, he is doing his job really well," the former Holland international said.
"Sometimes you have slip-ups but they are 15 points clear so that says enough. I know Lenny a little bit and he will want to win the cup and get the double.
"As a footballer, there is a competitiveness, you want to win. It is like an addiction and if you win prizes you want to do it over and over.
"I think that is in the mind of Lenny and hopefully in the minds of a lot of players."