On Q's second visit to the Enterprise, he tells a complete untruth.
PICARD: Pay off your wager.
Q: I recall no wager!
TNG: Hide and Q
During his third visit, he lies again since (we later learn) humanity has remained on trial throughout the entire voyage of the Enterprise-D
RIKER: The good times? The first time we met you, you put us on trial for the crimes of humanity.
Q: Of which you were exonerated.
TNG: Q, Who?
He tells a fib in his 6th encounter, stating that Amanda's parents died in an accident when in fact they were murdered.
TROI: What happened to Amanda's parents?
Q: They died in an accident.
TNG: True Q
He lies to Vash in TNG: Q Less. Clearly the inhabitants of Brax hate his guts.
VASH: You're the one who almost got me killed on Errikang Seven. And they weren't exactly thrilled to see you on Brax either. What did they call you? The God of Lies?
Q: They meant it affectionately.
He lies to Janeway in VOY: The Q and the Grey. There's no evidence that he's actually ordered anything at all from the kitchen.
JANEWAY: Janeway to security. Intruder alert.
Q: There's no need to call room service, Kathy. I've already ordered.
The Q and the Grey