Hello Welshgirl,
I take it you have not seen Robert Neil, and Lillias's, marriage certificate 1868. Kilmarnock, this would confirm who her parents were, you can purchase this certificate for a small sum on Scotlandspeople.
On the 1851. census Kilmarnock, Ayr. you have the Kellahin, family. this is only a index not the full census.
Kellahin Robert, 67 years,
Kellahin Mary, 67 years,
Kellahin John, age 48 years,
Kellahin Lily, age 24 years,
Reid Elizabeth, age 14 years,
Mahalam Liley, age 4 years.
This index was transcribed by the East Ayrshire, FHS. by volunteers so the details may not be 100% correct, ie ages, etc.
I have checked the index on Scotlandspeople, and Mahalam Liley, age 4 years is correct.
Its quite possible Liley, was born prior to her mother Ellen's, marriage to Joseph Mulholland, and thats why her surname is Mahalam.
So getting the marriage certificate will clarify the names.
Remember also its Irish, folks we are discussing here and there will be lots of variations on names.
Regards,
Jonn.