The smart move may be to move Youkilis to third and bring in a first baseman. There aren't many good third basemen available on the free agent market. Aaron Boone is, though
Menkeiwich is available and probably for a song. You could sign him for his glove and use him the way they used him in 2004. Then you could also try to sign a bopper for his bat, like a Hillenbrand or a Tony Clark, and still have $10 million in your pocket over what A-Rod would cost. Or you'd get those two for what re-signing Lowell would cost.
The sticking point with Lowell won't be the bucks---they Sox would be perfectly willing to commit to $25 million over two years. It'll be the years. Reportedly, Lowell wants $40-$48 million over 4 years. If the Yankees don't give it to him, chances are the Phillies will.