Why did he say "Te'alamnah Sifsei Sheker"?
Bava Metzi'a 75b: Anyone who lends money without witnesses transgresses "Lifnei Iver" and brings this curse upon himself. (It is as if he becomes mute, for the borrower will deny, and people will suspect that he falsely claims from him.)
Radak: The lips that say Sheker about me, and tell Sha'ul that I am haughty and glorify myself in kingship [should be mute].
Sha'arei Teshuvah 1 (4:21): One may not confess again on Aveiros for which he confessed on a previous Yom Kipur. This shows that he does not believe that Hashem is Nosei Avon.
Malbim: After he saw Hashem's Hashgachah on him, he will say that false lips, i.e. of the deniers, will be silenced. Now they will see how You save those who hope in You.
This is according to one Tana. We follow the opinion that it is good to do so to fulfill "v'Chatasi Negdi Tamid" (51:5) (MB 607:14).
What is the meaning of "ha'Dovros Al Tzadik Asak"?
Rashi: They tell Sha'ul 'David seeks your evil.' Asak is Sarah (Sheker), like "va'Ya'atek mi'Sham" (Bereishis 12:8).
Rashi citing Dunash: Asak is something great and hard, like "Asku Gam Gavru Chayil" (Iyov 21:7).
Radak: They speak about me and other Tzadikim a matter of pride and strength.
Malbim: [The deniers] speak about Hashem ha'Tzadik with arrogance and contempt. They say that He does not supervise His world, and there is no reward and punishment, and the world is Hefker (people may do anything they want).
