Hi Karen
He was born in Castleford which came under Pontefract registration district.
Keighley is just one of many registration districts in the West Riding
Firstly - Although Emma's maiden name was Lucas, what you don't know is whether she married before she took up with George Lilliman. She certainly had children before Lilliman - Henry for one - so where was he in 1881 as you say you have found Emma unmarried in 1881. Henry was born 1878/79 but there is no corresponding birth on freebmd in Pontypool for a Henry Lucas. I would guess that Peter was pre-Lilliman as well but there is no Peter Lucas birth in Yorkshire 1881-1883
Both the 1891/1901 shows Emma b Ludwell Wiltshire whereas the 1881 entry you mention shows her b Donned and working in Kent
We can't find a Lilliman marriage to Emma but she re-married to Davies as Emma Lilliman
Here's what I think - but still to be proved
Emma Lucas married and had Henry and Peter - we haven't a clue who she married or where
She was then widowed (don't know when) and married George Lilliman. I suspect James was Lilliman's son