I've just dug out my copy of Almondbury Places and Place-Names by George Redmonds.Redmonds is very much the doyen of place and surname studies in these parts.
In discussing the road running past Castle Hill towards Farnley:
Between Castle Hill and Jackroyd the former highway is now known as High Lane and there is no doubt this is the old name...The "house called Ashes adjoyning to Castle Hill" had been, in 1583, "late purchacyed by John Kaye"...1584...Giles Kaye held this property [and] Leston Royd ..."on the south side of Hilane".
He goes on to interpret the 'Kayes of Lane' to which you referred as the Kayes of this area. Then: ...and finally, in 1716, Kay Lane emerged as a place-name.Ashes Lane and Jack Royd Lane both of which now apply to sections of the former highway, seem to be later developments.