Christina Scull and Wayne G. Hammond have suggested that dwimmerlaik derives from Middle English dweomer, Old English (gwe)dwimor, -er ("illusion, phantom") + Middle English -layk, -laik ("play"). See also Dwimordene, Dwimorberg.
It is not clear if the word refers to a creature of the Rohanese folklore (like the holbytlan), specifically a phantom; therefore when Éowyn confronted the Witch-King she likely rather identified him with one, than coining the word on that moment.
David Day in A Tolkien Bestiary considered that a Dwimmerlaik is any creature of Rohanese superstitious folklore that includes Elves and Ents. However, other than the appearance of the root dwimor- to describe Lothlórien, there is no indication in Tolkien's writings that the word pre-existed or that it was used for other races.