What does Psalm 35:11 mean?

No exact event in David's life is connected to this psalm. However, part of the persecution he faced was the use of malicious witnesses (Psalm 27:12; Exodus 20:16). Whether this involved an actual court case, or simply people attacking his reputation, we are not told. Both Saul (1 Samuel 19:1–2) and Absalom (2 Samuel 15:13–14) likely spread propaganda and falsehoods about David as they tried to win people over to their side. Wherever the lies were being spread, they were a farce. David was not sinlessly perfect, but he was certainly innocent of the charges brought against him. In fact, David isn't even aware of the issues they raise.

Again, what happened to David foreshadows what happened to Jesus. We read in Matthew 26 that after Jesus' arrest the entire council, the Sanhedrin, tried to coordinate false testimony against Jesus. Their goal was not truth, but to put Him to death. Despite many lying witnesses, they couldn't arrange a coherent accusation. Finally, two came forward and reported that Jesus had said, "I am able to destroy the temple of God, and to rebuild it in three days." When Jesus said the high priest would see the Son of Man seated at God's right hand and coming in the clouds, the high priest accused him of blasphemy. He and the council concluded that Jesus deserved death (Matthew 26:57–66).