David is speaking about himself. This can be stated clearly in the translation. Alternate translation: "I, the king of Israel, will" (See: [[rc://en/ta/man/translate/figs-explicit]])
Here "the mouth" represents the whole person. This can be stated in active form. Alternate translation: "but God will silence the liars" or "but God will silence those who lie" (See: [[rc://en/ta/man/translate/figs-synecdoche]] and [[rc://en/ta/man/translate/figs-activepassive]])