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.

O Lord, open thou my lips - My heart is believing unto righteousness; give me thy peace, that my tongue may make confession unto salvation. He could not praise God for pardon till he felt that God had pardoned him; then his lips would be opened, and his tongue would show forth the praise of his Redeemer.

O Lord, (n) open thou my lips; and my mouth shall shew forth thy praise.
(n) By giving me opportunity to praise you, when you will forgive my sins.

O Lord, open thou my lips,.... The Targum adds, "in the late"; which were shut with a sense of sin, with shame of it, and sorrow for it; and though they were in some measure opened in prayer to God for the forgiveness of it, as appears by various petitions in this psalm, yet he still wanted a free spirit and boldness at the throne of grace, which the believer has when his heart is sprinkled from an evil conscience by the blood of Christ; and especially his lips were shut as to praise and thanksgiving; the guilt of sin had sealed up his lips, that he could not sing the praises of God as he had formerly done; and only a discovery of pardoning grace could open them, and for this he prays:
and my mouth shall show forth thy praise: the praise of his mercy, grace, goodness, truth, and faithfulness, in psalms, hymns, and spiritual songs; see Psalm 103:1.

open . . . lips--by removing my sense of guilt.

My lips - Which are shut with shame and grief.