Simply put, I don't think this is about this year, but next year.
Lynch is likely to get cut next year and unlikely to find a deal that pays him what his contract states. That's just business. If the team "forces" him to play his current deal and then cuts him next year, it's bullshit really. So from Lynch's perspective, it makes sense to hold out. I want to keep my players happy - and at the moment I still feel there's a bit of ill-feeling in the dressing room regarding the way Bryant and Clemons were treated. Lynch has been one of the best players in the league at his position, and rightfully so he's been paid like one, but there's still significant talent left there that Lynch could get paid better for elsewhere.
I look at it this way - if Lynch was to hit the open market as a free agent today, would he get a better contract over the next 2-3 years than he's scheduled to make? Yes, absolutely. So pay him like it. Next year? Maybe not. We know he plays a physical game, and this year could be the last year he has the bargaining power for a big deal.
For those that say "he's made his money over the last 2 years, now it's a team friendly deal for the next 2 years", if that's the case, teams should never cut anyone who gets a deal that's team friendly for the first half of a contract before they earn the big dollars at the end. It goes both ways. Lynch is entitled to do what he's doing, he's been the best running back since mid-2011 and has been paid like it. Continue to pay him like it or watch him retire.