In 1 Corinthians 7:39, Paul writes, " The wife is bound by the law as long as her husband liveth; but if her husband be dead, she is at liberty to be married to whom she will; only in the Lord." Does "in the Lord" in this verse mean that the wife, who is free to marry, must marry only a Christian man?
The phrase "in the Lord" occurs forty-seven times in the New Testament. Sometimes it does refer to people who are "in the Lord" where the phrase means that they are in the body of Christ--members of the church--Christians. One such example is in Romans 16:8 and 11. Here Paul is saluting members of the church and he describes them with short epithets. In verse 8 he says that Amplias is his beloved, in the Lord. In verse 11 he says that the house of Narcissus are in the Lord. These references certainly refer to individuals who are Christians and the phrase "in the Lord" here means "a Christian." This is pretty much the case when the phrase is being used to describe a noun, pronoun, or relative pronoun to describe the location of the person or to answer the question, "Where does this person reside?"
However when a phrase is used with a verb it can mean that the action that is being referred to is to be authorized by Christ or that the action should be done within the confines of the teaching of Christ. Take the following passages as examples. In 2 Corinthians 10:17, Paul writes, "But he that glorieth, let him glory in the Lord." Here the prepositional phrase is referring to the verb "glory." Instead of referring to location, it describes the instrument by which the main verb is to be accomplished. So in 2 Corinthians 10:17 Paul writes, "But he that glorieth, let him glory." How? "In the Lord." By the authority of the Lord; according to the instructions of the Lord; only as the Lord dictates. The idea is that the phrase answers the question, "How should I accomplish the main verb?" Another outstanding example of this kind of usage would be in Ephesians 6:1. "Children, obey your parents in the Lord, for this is right." This passage is not saying that children may be disobedient to parents who are not Christians, but rather, that children are to obey their parents as they instruct them by the authority of the Lord.
Now when we get to 1 Corinthians 7:39, the context is a little ambiguous. Is the phrase, "In the Lord" used in the sense of answering the question "Where" or in other words, "To whom the widow shall marry?" Or, is the phrase used in the sense of "How" or in what manner is she to be married?
Those who argue that this means that she can only marry a Christian say that it would not be necessary for Paul to say that she can only marry by the authority of the Lord--that should be obvious! However, given that Paul has been discussing all of these different marriage situations and now he comes down to this last final situation, he wants to make it clear that he is not authorizing a widow to just go out and marry whomever she pleases regardless of the potential spouses previous marriage situation. Rather, Paul wants her to make sure that she abides by the Lord's instructions regarding who may marry. So she may only marry someone whom the Lord has authorized to marry.
Does this person have to be a Christian? I don't think this is what the passage means. However, if you are in this situation, my advice to you is that if you are NOT SURE, then choose the safe course. Marry a Christian. It is not worth taking the chance and losing your soul.