Maybe they bid more, but less years. And Lester will be a tough nut to sell to come to a team right now like the Cubs. Granted, they are way ahead of the game with the potential talent, and Rizzo and Castro are set at their positions (I think), but Boston was his home, and the fact that they have a good minor league system like the Cubs, he could step right back into familiarity with his old team mates and make more money than he has in the past. He has his two rings also.
The question might be, what is the lure to come to Chicago? The clubhouse isn't ready. The team isn't ready (not much different than Boston, but they are closer with the vets). And the FO for Boston is showing that they are willing to spend or be aggressive right now as evidenced with Rusney Castillo, and the laid out contract with Lester, and the apparent bid for Sandoval.
The Red Sox don't have to sell him much. The Cubs however, do.