Hi,
Here are some of the things I have come across with my lot ( besides the misspelling of names), it may be of some help to you :
It may be something as simple as they did not fill in the 1901 census ( I couldn't find my grandmother on the 1901 census, her father didn't fill one in)
Or do you know for sure that your grandmothers parents were married and living together at the time of the census
This happened to me with my great grandfather. I had my Great grandfathers birth certificate and the name of his father on the cert . My G grandfather was registered under the fathers name on the birth certificate, but I could not find him anywhere at all on the 1881 census when he was a 9 year old child. So I put in my G Grandfathers mothers maiden name - and low and behold I found his mother with my G grandfather
The mother was unmarried and was with my 9 yr old G Grandfather on the census under her maiden name .The named husband which I had on the birth cert was living a few doors down. My G.G Grandmother was lying when she registered my G Grandfathers birth under the fathers name ( they eventually did get married, I found a marriage cert for them 4 years after the census I was looking at) . So you can't always go by what is written on that birth certificate. your grandmother and her mother may be on the census under that maiden name.
Try searching for your grandmother under the maiden name of the mother "Lilly or Llilian Barnfather" ( and also misspell that surname too - it looks like a name that could get misspelt on the census) you never know..
Another idea , has your grandmother got a middle name? she may be listed under her middle name - for example one of my relatives his name is David John, On two of the censuses he is listed under his middle name John and not David. This happens quite a few times with my family.
Or, perhaps your G grandfather died, and your G grandmother was re-married on the 1901 census, and listed your grandmothers name on the Census under her new married name for some reason.
Or just resign to the fact they may not be on there, it can be something as simple as that. I know that one of my grandmothers who was born in 1900 is not on there. Apparently her father was always moving them about in those days, running from something ( my grandmother told my mum years ago that her father moved her about to avoid the inoculations.. that to me sounds very unlikely, he probably was avoiding debt, or the law for some reason)
There could be a million reasons, very frustrating isn't it with some of these lines. Some of mine I've had no problem with at all, going back to the 1600 and 1700's so far , but other lines of mine are a nightmare, they seem as if they don't want to be found
good luck

Could this be her misspelt ? ( north East Yorkshire though, I think where Middlesbrough is.. I'm not very good with the geography of England)
Lillian Brampton 4 Yorkshire Middlesbro Middlesbrough Middlesbrough
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John Brampton 42 Yorkshire Skelton In Clerelord Middlesbrough Middlesbrough Railway Engine Driver