We don't know, and there's nothing that gives us an indication.
I've searched all the books, and not only does this not happen anywhere in the books, there aren't any situations that even give us a clue what might happen in this case. Presuming that the person is unable to resist both Veritaserum and the Imperius Curse, which is likely enough as an insufficiently strong-willed person couldn't fight the effects of either, there's no way to know which one would "win" based on information we have rather than just speculation.
For example, the Thief's Downfall washes away enchantments, including both a fairly complex potion (Polyjuice Potion) and the Imperius Curse.
“The Thief’s Downfall!’ said Griphook, clambering to his feet and looking back at the deluge on to the tracks, which Harry knew, now, had been more than water. ‘It washes away all enchantment, all magical concealment! They know there are impostors in Gringotts, they have set off defences against us!’
Harry saw Hermione checking that she still had the beaded bag, and hurriedly thrust his own hand under his jacket to make sure he had not lost the Invisibility Cloak. Then he turned to see Bogrod shaking his head in bewilderment: the Thief’s Downfall seemed to have lifted the Imperius Curse.”
However, this doesn't give any indication what would happen if someone was given Veritaserum and then Imperiused to lie.
It's also not a reasonable assumption that whichever was used last would just "cancel out" the first one. Some magic is strong enough to resist other magic being used against it, and we don't know how powerful Veritaserum is compared to the Imperius Curse.
The Imperius Curse is powerful...
“Total control,’ said Moody quietly, as the spider balled itself up and began to roll over and over. ‘I could make it jump out of the window, drown itself, throw itself down one of your throats …”
Yet it can be resisted:
“The Imperius Curse can be fought, and I’ll be teaching you how, but it takes real strength of character, and not everyone’s got it. Better avoid being hit with it if you can. CONSTANT VIGILANCE!’ he barked, and everyone jumped.”
Veritaserum is also powerful:
“No,’ said Harry, completely honestly this time.
‘It is Veritaserum – a Truth Potion so powerful that three drops would have you spilling your innermost secrets for this entire class to hear,’ said Snape viciously. ‘Now, the use of this Potion is controlled by very strict Ministry guidelines. But unless you watch your step, you might just find that my hand slips –’ he shook the crystal bottle slightly ‘– right over your evening pumpkin juice. And then, Potter … then we’ll find out whether you’ve been in my office or not.” - Harry Potter and the Goblet of Fire, Chapter 27 (Padfoot Returns)
There's no mention of Veritaserum being resisted in the books, so it might have an edge over the Imperius Curse.
However, in JKR's FAQ, she says that Veritaserum can be resisted as well, so if you consider non-book information canon, then they're pretty much equal again.
Veritaserum works best upon the unsuspecting, the vulnerable and those insufficiently skilled (in one way or another) to protect themselves against it. Barty Crouch had been attacked before the potion was given to him and was still very groggy, otherwise he could have employed a range of measures against the Potion - he might have sealed his own throat and faked a declaration of innocence, transformed the Potion into something else before it touched his lips, or employed Occlumency against its effects. In other words, just like every other kind of magic within the books, Veritaserum is not infallible. As some wizards can prevent themselves being affected, and others cannot, it is an unfair and unreliable tool to use at a trial.