The player can do that. The specific technical term for it is Cheating.
The DM has to keep track of the entire world, and what all the different NPCs are doing. The DM is supposed to be keeping track of sense motive checks, will saves, detect magic, zone of truth, etc. Was the dias upon which he made those oaths enchanted with a Zone of Truth spell under specific circumstances? The player doesn't know! The DM does.
What's more, this isn't just about motivations. This is about actions. A lie is not just a 'motivation'. It is an active performance. Did the liar ... fail to hold eye contact? Hold too much eye contact? What did he do with his hands? Did he sweat? Did his eyes make rapid little movements? did he fiddle with his hair? Did he twiddle his fingers? Did he rub his hands on his trouser seam? Did his intonation sound natural, or was it too fast or too firm? Did he oversell it? Undersell it?
If he did ANY of these wrong, then this is no longer a 'normal' situation, and he is not acting as expected. He is telegraphing that he's lying.
Someone skilled at seeing through lies (with a high score in their Insight) will see all of this and more, as naturally as a non-colorblind person can see that the shirt that the liar is wearing is blue. Happily, you don't have to keep track of all this because there's a convenient mechanic in place: Bluff vs. Insight.
So yes. The player can cheat. The question is: does the DM put up with cheaters at his table, and consider that to be a fair gimmick? Metagaming and all that. I've known some groups which had it considered a basic house rule that 'If you can get away with it, then you can do it,' no matter what the rules said. You have to ask yourself what you and your group feels about cheating.
Now, I have a suggestion for you.
The player's character is now under a geas.
He didn't know it, but the dias upon which he made that oath was enchanted to hold people to their words. If he breaks his oath, or even TRIES to break his oath, then he suffers the results of a broken geas until he redeems himself somehow. He gets no save because he voluntarily entered the space of the geas. And also because he didn't bother telling you that he was lying.