Does a person run or stand for election? I have a sentence that reads: "Now is the time to start thinking of standing for election to a lodge office." I have been told that it should read: "...run for lodge office." Is that true?
In the US, run for office is much more common than either run for election or stand for election. Consider this NGram (American English corpus):
Thus, if you are in the US, I'd agree with the correction you were suggested, especially since run for [office] can be and usually is used with the name of a specific office. Since your sentence talks about not just a generic election, but election to a lodge office, it seems a little redundant to say standing for election to a lodge office when you could just say running for a lodge office.
Addendum: Though this wouldn't really fit in the example sentence you gave, if you want a stock phrase of similar meaning that uses the word election, Americans often say that a person is up for election. e.g. "Bush was up for election in 2000, and again in 2004."
Running up the Google N-grams:-
suggests that stand for is more common than run for, although the difference is less marked when one selects the American English option:-
Here what the writer Emmet Fox (born in Ireland, raised in England, lived in the USA), wrote in 1953 on the difference between "stand" and "run":
Take politics, for example. Many people have a “slight” tendency to excessive criticism of the other side! Have you noticed it—especially around election time? Now that is a serious matter because if it is not checked, democracy may become impossible. In democratic countries, if a candidate is going to be vilified and accused of every crime under the sun, if a man stands, or runs—in England you stand for Parliament but in America you run for Congress (difference in tempo, you know)—if, as soon as a man runs for governor, or mayor, or senator, or president, if he is going to be accused of every foul thing, what will happen? Decent, sensitive men will not run for public office. Only the toughest people will do it. If the men who are really qualified in every way, with a high sense of honor, are going to be vilified like this, they will not run for office. So it is very important not to attack people in politics in that unfair way. I do not mean that they should not be criticized. You can say that Jones’s policy is bad, but not that Jones is a crook or that he beats his wife, when you have seen Mrs. Jones and know quite well that it is probably the other way around!
Excerpted from: The Ten Commandments: The Master Key to Life, Harper and Row, 1953