As far as I can see the admission criteria used by Lincolnshire are as follows:
A Looked after children
B Siblings
C Children of the faith (faith schools only)
D Children for whom it is the nearest school
E Other children
Distance is the tie breaker. Distances are the shortest driving distance along public highways.
I presume your daughter should have been in category D or E. Classmates living further away could have got in if they have siblings at the school or if they are actually closer to the school measured by driving distance. They could also have got in if your child was placed in category E whilst they were in category D. However, if they were in the same category as your daughter and were further away by driving distance that would indicate that a mistake has been made.
The questions you need to ask the council:
In which admissions category was your daughter placed for this school?
If she was placed in category E and you would have expected her to be in category D, which school do Lincolnshire regard as her nearest school? If she is in the wrong category that would be a mistake.
What is the measured distance from your home to the school and what route did they use? If you can find a shorter route using public highways that means they may have made a mistake.
What was the distance for the last child admitted and which category were they in?