O Lord, open thou my lips - That is, by taking away my guilt; by giving me evidence that my sins are forgiven; by taking this burden from me, and filling my heart with the joy of pardon. The original word is in the future tense, but the meaning is well expressed in our common translation. There was, in fact, at the same time a confident expectation that God “would” thus open his lips, and a desire that he should do it.
And my mouth shall show forth thy praise - Or, I will praise thee. Praise is the natural expression of the feelings when the sense of sin is removed.