Gu Qianqian's past is too complex; outwardly her mother is the adopted daughter of the Lu family, but everyone in the Lu family knows she had an affair with Lu Zhendong in her youth.
She was initially driven out of the family home because she unexpectedly got pregnant. Even though no one ever publicly accepted it, the Lu family internally admitted the fact that Gu Qianqian was really an 'illegitimate child'.
As a member of the Lu family, Lu Zhanbei was also aware of this, so from his standpoint, Gu Qianqian was not an illegitimate child.
Knowing Lu Zhanbei's independent nature, once he had an idea, he would likely have nothing to hold him back.
Luckily, Lu Zhanbei knew nothing about Gu Qianqian's real identity. Having this in mind, there's no way he would fall for Gu Qianqian.
But the problem was, the daughter knew nothing!
She still thought she was from the Gu family, therefore she felt there was no relation between her and Lu Zhanbei.