Reading the earlier ones there in Itivuttaka: The Group of Ones, you can see things like,
Abandon one quality, monks, and I guarantee you non-return. Which one quality? Abandon greed as the one quality, and I guarantee you non-return.
Next it says,
Abandon one quality, monks, and I guarantee you non-return. Which one quality? Abandon aversion as the one quality, and I guarantee you non-return.
And,
Abandon one quality, monks, and I guarantee you non-return. Which one quality? Abandon delusion as the one quality, and I guarantee you non-return
This is referring to the three poisons which are shown as being at the centre of the 'wheel of life'. My understanding, from the way they're represented/illustrated, is that they cause or feed each other.
Wikipedia claims that ignorance is the root cause:
Of these three, ignorance is the root poison. From ignorance, attachment and aversion arise.
Whether or not it is the "root" cause, the implication of the suttas above is that if/when you can eradicate any one of them then you can break the chain or cycle.
The corollary though, IMO, is that if a person indulges in or abides in any one, then they cause them all.
The second noble truth explicitly warns against greed, but the 'three poisons' also warn against anger and ignorance.
And it seems to me that lying is (except in vanishingly rare circumstances) intended to promote ignorance. A person who thinks they can lie successfully might think that they can 'get away with murder'.
You ask, "Is it exaggerated?" IMO 'not lying' is also connected with Right Speech, with being able to share (true) Dharma, with not causing schism in the Sangha.