Hello lalaus,
Welcome to Roots Chat.
The records for the Cheshire Asylum, known locally as The Deva, are held in the Cheshire Record Office in Chester.
I imagine it would require a visit to inspect these. Before you make any journey, I would ask them about the terms of access as sometimes such records are closed (ie not available to the public) for 100 years. Since you have a close relationship, Lilian being your grandmother, I imagine that you should be able to view these but you may need to supply proof of that.
Jo