It's named after Lyme Hall. The colliery, Lyme Pit, was also named after Lyme Hall. So is Lymewood Court. And Lyme street.
Legh Pit was named after the family who lived, and still live, in Lyme Hall. So was Legh Road.
The Legh family, of Lyme Hall, owned Haydock. Actually, they still do!