We do not currently know of any synonyms for lyrebird.
The noun lyrebird is defined as:
Either of two large ground-dwelling Australiansongbirds, of the genus Menura, named because of the beautiful tail feathers of one species, the superb lyrebird (Menura novaehollandiae) which can be erected to look like a lyre, most notable for their extraordinary ability to mimic natural and artificial sounds from their environment.