Back in Wano Kaido it said that awakening occurs when your mind catches up with your Devil Fruit, and although that’s a description, it’s still ambiguous in my opinion.
However, Vegaponk in chapter 1069 talks about how Devil Fruits are born from desires, so it’s possible that the desire to be free or something like that created the Neca Fruit.
Now here’s my theory: in order to awaken a Devil Fruit, you have to embody the original desire that created the fruit, or at least understand it. Luffy couldn’t awaken his Devil Fruit until he truly desired to be a liberator, afraid of the future of the Wano people under Kaido if he lost.
This may also explain why awakening Zoans is dangerous, as the urge to become an animal will slip out of your mind if you’re not careful. My theory is that Lucci wasn’t overwhelmed by Ted’s innate nature because he represented it really well. His fruit is that of a tiger, a predator who wants to kill, Lucci actually wants to kill, he is violent and serves the world government so he can kill those who order him to, so when he woke up he wasn’t so overwhelmed. The nature of the fruit because that was his nature indeed.
* theory Nicentra