C. F. Keil and Franz Delitzsch on Lamentations 3:29

Lam 3:29 "Let him put his mouth in the dust," i.e., humbly bow beneath the mighty hand of God. The expression is derived from the Oriental custom of throwing oneself in the most reverential manner on the ground, and involves the idea of humble silence, because the mouth, placed in the dust, cannot speak. The clause, "perhaps there is hope," indicates the frame of mind to be observed in the submission. While the man is to show such resignation, he is not to give up the hope that God will deliver him from trouble; cf. Job 11:18; Jer 31:17.