He's also lower cost because he's not as good as Kluber, Cueto, Bumgarner or Price, to name some of the big October pitchers from the last few years and one of the big deadline acquisitions, or other big buck pitchers. Lynn may be "worth the money," and he could be part of an October rotation, but he's not going to be the leader, which is what the Twins need.
He's also entering the decline phase of his career, so Falvine may not want to buy an extended commitment to Lynn.
Almost every FA pitcher will be entering the decline phase during their FA contract. It's part of the price of getting really good FAs for more than 2-3 months in a trade.