Can the noble eightfold path be followed in its entirety by a lay follower? Does the noble eightfold path fits a lay life perfectly? Or is there any part of it that cannot be followed/accomplished by a lay buddhist?

If that's the case, what part(s) doesn't have fit with lay life?
At a higher level the 8 fold path consists of 3 fold training:


Development of morality
Development of control or mastery over the mined
Development of knowledge of the reality pertaining to one's mind and cognitive process


There is nothing in the above which a lay person cannot develop or not reap benefits by developing.

Being a monk you have less responsibilities hence more time to practice. The key is to practice regardless of whether you are lay or a monk.