This can be stated in active form. Alternate translation: "The troubles of those who seek other gods will increase" (See: [[rc://en/ta/man/translate/figs-activepassive]])
Lifting up their names is a metaphor for praising them, and "lips" is a metonym for what one says. Alternate translation: "or praise them with my words" or "and I will not praise their gods" (See: [[rc://en/ta/man/translate/figs-exmetaphor]] and [[rc://en/ta/man/translate/figs-metonymy]])