He joined the board in 1988 and became chairman in 1999, overseeing the best period in the club’s recent history with a succession of top-10 Premier League finishes which brought European football.
However, relegation in 2012 contributed to serious financial problems and Bolton currently sit four points from safety while facing a winding-up order.
Former Celtic boss Lennon said: “I would like to think the players would make a stand for Phil now and do something positive in his memory. And that is to survive.
“We’ve given ourselves a foothold in the race. We’ve got some difficult fixtures to negotiate, but there’s an extra motivation now – as if we needed any more.
“I know some of the players were close to Phil as well and had a great relationship with him, so, hopefully, through all these bad times there might be something good to come out of it in terms of driving the club forward.”
The Irishman, who took over as boss in October 2014, added: “All the other stuff pales into insignificance compared to what I’m feeling about the loss of Phil.
“I was very close to Phil for over a year. We knew for a while he was gravely ill, but it’s still a huge shock when it comes and it’s devastating, not just for myself and my backroom team, but the whole of the club because he was such a huge figure here for a long time.
“I always felt he had great ideas on the game, whether it was what he wanted to achieve here at Bolton or for the game in general.”