There are quite a few free agents that should be attractive to the Red Sox this off-season. Because of that, we'll take them one at a time, and profile those who Boston might be a match with. Just because they're covered here, though, doesn't mean they're endorsed: this is meant to be an exercise in finding out whether or not the players in question should be future Red Sox.
Kyle Lohse was a huge part of the St. Louis Cardinals' rotation the last two seasons, on a club that won a World Series and then took the NL Central the next year. After a rough 2010 campaign, Lohse combined for 399 innings, and a 3.11 ERA in 63 starts between 2011 and 2012. Because of this resurgence, and a stretch that is the best he's had in his career, Lohse is looking for a serious contract this off-season. For a team that fails at signing Zack Greinke and Anibal Sanchez, Lohse might represent an attractive alternative.
There should be heavy emphasis on the "might" there, though, as there are plenty of reasons why Lohse was a product of his environment. It's more than just the park he was in, as nearly everything involved in being a St. Louis Cardinal made him as valuable as he's been, in ways that won't necessarily translate to the Red Sox.
That park, Busch Stadium, is very pitcher-friendly. The right-handed Lohse pitched in a park that stunted production from left-handed hitters, and annihilated power for those hitting from the right side. From 2008 through 2012, the years Lohse was in St. Louis, he allowed a line of .248/.294/.384 at home, and an awful .285/.329/.450 on the road. In the last two seasons, when he's been a better overall pitcher for the Cards, that split was .231/.278/.358 at home, and .255/.286/.398 on the road. That's better, but it's not enough, and as said, there is more influencing his production than just park.
The National League has no designated hitter, meaning the pitcher gets to hit. Pitchers are an easy out, but they are an easier out for some than for others. Your average pitcher in the National League allowed a .172/.223/.242 line (465 OPS) to the ninth hitter in the batting order in 2012. Lohse gave up just a .145/.181/.145 line (325 OPS) in the same time frame. That might not seem like much, but it's 140 points of OPS in 81 plate appearances, or, roughly 10 percent of his total batters faced. In 2011, the difference was even greater, with Lohse allowing a 250 OPS to ninth hitters, while the NL as a whole gave up 482. Cut those appearances against pitcher's out entirely in 2011, and Lohse would have allowed a .262 batting average and .418 slugging rather than the .241 and .390 he actually managed. Throw in what an average DH hit in 2011 instead of the pitcher's line, and you'd likely see an additional negative effect.
How many rallies ended thanks to the pitcher spot, potential run-scoring situations that, in the American League, would not have been escaped so easily? Those plate appearances combined for one-tenth of a season's work, enough to assume that it would put a dent in Lohse's otherwise flawless record.
Combine that with the park effects, and Lohse starts to look like a bad fit for the AL, never mind in a hitter's park like Fenway. When you bring the change into division into play, that's strike three, Lohse is out. The American League East and West are two of the toughest divisions to pitch in, something that can be gleaned from looking at the pitcher's quality of opponents report at Baseball Prospectus. This measures how productive offensively the collective opponents of a particular pitcher have been. Lohse's opponents had a 759 OPS in 2012, putting him in the middle of NL pitchers with 100 innings pitched, and in 2011, his 749 showing was similarly ranked. He didn't have the most luck in his schedule by any means, but he also didn't have to face the lineup onslaught that he would were he to enter the AL East fray.
Let's not discount his last two years entirely, though. Lohse has featured a two-seamer much more since 2011, and it's been effective for him, especially in 2012. While his grounder rates are no higher, he's posted better-than-average batting averages on balls in play the last two seasons. There could be a correlation here between the pitch and inducing weaker contact, but in this small sample, it's hard to say. Therefore, it's hard to commit buckets of money and multiple years to the idea, especially considering all of the boosts from context discussed above.
Lohse could be a useful back-end rotation option, a fourth or fifth starter that could throw 190-200 innings over 30 starts or more while being fairly average while doing it. He's looking to be paid as more, though, and on a long-term deal. That's not in Boston's best interests for either now or their future, meaning the only way they should pay attention to him is if he's still available on a one-year deal a couple of months from now, and other, potentially more-productive plans have gone by the wayside.