William and Lillian are definitely too similar, even the nns (Will and Lily). Since you have other boy names you like, I'd keep Lillian and use either Miles or Lucas.
Miles and Lucas are not options (a note on the nns...)I've crossed them off the list. However, we do have other boy names...William will not have a nn from the family, and Lillian will never by Lily unless that is what she wants when she is older.