When used to address others, roughly equivalent to "shut your mouth."
In self-reference, the phrase takes on the connotation of withholding a secret or some other information, i.e. "My lips are sealed".
Dated phrase referencing back to the keyholes mounted on metal plates below doorknobs, the locking of which would resound with a reaffirming 'tick'.
"Tick a Lock, Landsman," Cashdollar says softly, miming the twist of a key in the hole of his mouth.