"Lunar New Year" is perhaps over-general, since there are non-Asian lunar calendars, such as the Hebrew and Islamic calendars.
That said, "Lunar New Year" is probably as good a compromise as any, since we have other names for the Hebrew and Islamic New Years.
There's more than one Asian lunar calendar: https://news.ycombinator.com/item?id=46996396.
The Islamic calendar originated in Arabia. Calling it an Asian lunar calendar wouldn't be inaccurate.
This all seems like a plot to get everyone worshipping the Roman goddess Luna.