John Gill Commentary Psalms 51:15

"O Lord, open thou my lips; And my mouth shall show forth thy praise." — Psalms 51:15 (ASV)

O Lord, open you 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 your praise :
the praise of his mercy, grace, goodness, truth, and faithfulness, in psalms, hymns, and spiritual songs; see (Psalms 103:1–3) .