"I will no longer remember their sins and lawless deeds.'" or "I will no longer think about their sins and lawless deeds.'" This is the second part of the Holy Spirit's testimony (See: [Hebrews 10:15-16](./15.md)). You can make this explicit in the translation by ending the quotation at the end of verse 16 and starting a new quotation here. Alternate translation: "Then next he said, 'Their sins and lawless deeds I will remember no longer.'" (See: [[rc://en/ta/man/translate/figs-explicit]])
The words "sins" and "lawless deeds" mean basically the same thing. Together they emphasize how bad the sin is. Alternate translation: "The things they did that were forbidden and how they broke the law" (See: [[rc://en/ta/man/translate/figs-doublet]])