That wasn’t Lewis’s definition, it was websters.
Supernaturalism is not dualistic. Supernaturalism posits that Mind has always existed and created nature, and holds nature in existence. The supernatural interacts with creation first by being the source of Reason, and secondly, though rarely, in the form of miracles (Judaism, Christianity, Islam). Deists believe in the supernatural but do not believe that it ever interferes with nature.
If naturalism/materialism and supernaturalism are both false then what is the third philosophical worldview?
Webster or whosoever. I care not.
Supernaturalism IS dualistic. The characteristics of mind: immaterial, eternal, undefiled. The characteristics material nature: dense, transient, sullied.
The postulate that mind “contains” nature or predates it is obvious claptrap, a kludge meant to bridge the unbridgable.
The alternative to both these is a natural world that partakes of a total set of characteristics which while knowable are not easily known, and which are neither eternal or transient, immaterial or material, pure or sullied, but which transcends all these imperfect attempts at description.
Call it what you like, this worldview at least has the imprimatur of age.