It seems like most US presidents were, professionally, lawyers or generals. With this in mind, is there a correlation between presidential success and profession?

Presidents who were previously lawyers and generals happened much more frequently before the 20th century. The majority of modern presidents, though, haven't been lawyers or generals.

Teddy Roosevelt was a former soldier and public intellectual. Woodrow Wilson only did law for less than a year before taking up a position as a professor of history. Warren Harding was in the newspaper business. Herbert Hoover was an engineer and economist. FDR only did law for a very brief stint before joining politics. Like Wilson, law practice had very little significance in FDR's life. Harry Truman was a small business owner before getting involved in local politics. JFK didn't have much in the way of any occupation before joining politics. Lyndon Johnson was a teacher. Jimmy Carter was a peanut farmer and teacher. Reagan was an actor and union leader before entering politics. George H.W. Bush was a businessman, as was his son. And while Clinton had a law degree, he never practiced for any significant period of time because he entered politics almost as soon as he got his law degree. Obama's being a practicing attorney before gaining the presidency is thus far from the norm.

The only modern president that had significant professional experience with practicing law was Richard Nixon, and I think we can say with a fair degree of certainty that his presidency wasn't successful (particularly on those issues of legality and constitutionality). If we include Taft in the era of the modern presidency, then we can also add him as having significant experience with practicing law before the presidency. Several more presidents did obtain law degrees but never practiced.The only general to eventually become president in the 20th century is Dwight Eisenhower. Within the last century the men who would eventually become president have held a wide variety of occupations, and because of that I don't think we can say that their previous occupations are a useful signifier of whether or not they will be successful as president.