The overt traits become latent, much like the Supreme Demons in Liu Hongzhao's world. They have the characteristic of being Undying and Indestructible in their native world, but lose their immortality once they leave, which doesn't mean it ceases to exist.
As long as it once existed, there will be traces of information, not to mention that the illusory hazy blossom itself is a unique information carrier.
This object is special in that the carrier also possesses 'universality', just like how Zheng Yichen's blood can model and reproduce life forms. Only when they are paired together does it count as a special kind of illusory hazy blossom.
Having only one of them is useless.
Lilith does not need to replicate the 'Power of the Heavenly Law' from another world; what she needs is a more comprehensive analysis and recording of the illusory hazy blossom, to replicate this trait and extract its advantages.