Lee was a key figure in London's successful bid to host the Games, alongside Sebastian Coe, but the pair have found themselves on opposite sides in the debate over how best to ensure a legacy for the centrepiece venue.
West Ham are also in the running to inhabit the stadium once the Games are over and would keep the running track as part of a 60,000-capacity stadium. Tottenham, meanwhile, would demolish the track and bid to contribute to an athletics legacy elsewhere by helping to redevelop Crystal Palace.
Park life: Tottenham hope to win the bid to build a new stadium on the Olympic Park site in Stratford
While Coe has publicly backed West Ham's bid on the basis that he feels a 'moral obligation' to retain a multi-sports venue, Lee - a former Hammers board member - is advising Spurs in their rival bid.
'If you're not in a great football stadium it affects your experience and your willingness to come week in, week out,' he told the Guardian, speaking of West Ham's proposals.
'The long-term future of athletics is also important. And we know that football and athletics don't work as a combination. Bayern Munich didn't have a great time in their Olympic stadium and athletics hasn't really worked there since the  Games. Espanyol were also happy to move out of Barcelona's Olympic Stadium.
'I genuinely think London has an opportunity to create the greatest Olympic Park ever. I'm not saying it's a simple decision. But if you duck difficult decisions when it comes to the legacy of these great sporting events you're in danger of creating a white elephant. In Olympic history those cities that have ducked difficult decisions have ended up regretting it.
On track: Spurs vow to rebuild Crystal Palace National Sports Centre to leave a legacy for athletics
'The Spurs and AEG link is economically very strong. I've long been convinced their combination, coupled with Spurs' pledge to build an athletics venue at Crystal Palace, is the best solution.