For example, when someone who doesn't normally lie starts lying and soon it's something that comes naturally to them.
Like when you lie so much that lying just becomes what you do and you can't really stop it.
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1A settled or regular tendency or practice, especially one that is hard to give up.
‘he has an annoying habit of interrupting me’ ‘good eating habits’
or in it's other form
1 Done constantly or as a habit.
‘his habitual use of heroin’
‘this pattern of behaviour can become habitual’
both from oxford dictionaries https://en.oxforddictionaries.com/definition/habitual
so for your example "he has become a habitual liar"
Apart from second nature that our friends have pointed out It can also be "parts of a person's character" or "propensity" :
e.g. He seems to have a propensity for lying all the time.
"someone’s middle name" is another suitable answer:
e.g. Lying and lying, this is always his middle name.
Or if you want to mention that someone will never change their behaviour or character, you can use"a leopard can’t change its spots":
e.g. A: Don't trust her - she's lying again. B: I know, a leopard can’t change its spots!