New York is the largest market in the world. All the Knicks needed to do to attract guys to sign was have capspace.
at the same time, they needed to reenergize the fan base and the city. Walsh in hindsight did an amazing job convincing New Yorkers to actually sit through a rebuilding phase and a roster purge to have a goal in mind of landing big time players for the hope of setting up their own super team. The Knicks play in NY, so a market can sell itself to a player, but the Knicks needed to sell themselves to the rest of the city. Amar'e for what it's worth, got people looking at the team seriously again, and then once Melo came, that's where fans felt like they could legit have title hopes again. As appreciated as Lee was, he just wasn't going to be the big splash that would have fans care again. Sucks for Lee because in a different summer or a different point in time, he'd still be a beloved Knick, but he was a casualty.
Knicks were looking for a player to build around, a franchise player. Lee wasn't gonna be that. Hell, Lee's not that for the Warriors.