This can be stated in active form. Alternate translation: "When they baptized Lydia and members of her household" (See: [[rc://en/ta/man/translate/figs-activepassive]])
Here "house" represents the people who live in her house. Alternate translation: "the members of her household" or "her family and household servants" (See: [[rc://en/ta/man/translate/figs-metonymy]])