I think that disturbing feeling you got was foreshadowing that something bad is gonna happen to Neil next chapter.
Seeing Neil still alive in the plot until Ep.10 worries me. What exactly is Neil's role in the plot? Just being the MC's father? I doubt it.
He lost the woman he loved for almost 20 years and decided not to get involved with any other woman since then, some players would like Neil to move on and meet another woman but that won't happen. He hasn't opened up to any woman in 20 years and he won't open up now.
I see two possibilities for Neil's existence so far: 1- He will die in the name of drama and to make the MC's development more significant, which is why DPC made Neil single to prevent the MC from having a widowed stepmother.
2- It will be revealed that Neil lied to the MC and it is actually Neil who forbids Lynette's family from having contact with the MC. Making the MC's grandfather the good guy in the plot and Neil the villain.