The word translated the people of her house (most translations “household”) has as its basic meaning “house” (see latter part of this verse), but it may also mean “family” (see 10.2). Since Lydia was the head of the house, it is assumed that she was either unmarried or a widow; and because her marital status is unknown, the people of her house perhaps suits the present context better than “family.” In rendering the expression the people of her house, it may be necessary to stipulate “the people who lived with her in the house.” In general this would include not only relatives but also servants and slaves.

If you have decided that I am a true believer in the Lord translates a conditional sentence in Greek that presupposes that the “if” clause is true to fact. That is, Lydia was saying, “Since you have decided….” True believer is literally “faithful,” which in the context describes one whose faith is genuine, and so is “a true believer.” In rendering true believer into another language there may, however, be a number of complications. In the first place one may need to place this into a verb expression “that I genuinely believe” or “that I really believe.” A term for true must refer to the quality of faith, not simply to some person who is “true” in character or who “tells the truth.” In combining the final phrase in the Lord with an expression for belief, one may have in some languages “that I truly trust the Lord” or “that I am one who truly trusts the Lord.”

Quoted with permission from Newman, Barclay M. and Nida, Eugene A. A Handbook on The Acts of the Apostles. (UBS Handbook Series). New York: UBS, 1972. For this and other handbooks for translators see here .