It's impossible to pinpoint one inventor of the first lunar calendar. Lunar calendars, based on the cycles of the moon, emerged independently in various ancient civilizations across the globe.

Here are some examples:

* Mesopotamia: The earliest known lunar calendars date back to around 3000 BC in Mesopotamia.

* Egypt: Ancient Egyptians also developed a lunar calendar around the same period.

* China: The Chinese lunar calendar, which is still in use today, has roots dating back to at least the 14th century BC.

* India: The Hindu calendar, with its lunar and solar components, has an ancient history.

It's important to note that these early calendars were likely not precise and underwent continuous development and refinement over time.

Therefore, attributing the invention of the first lunar calendar to a single individual or culture is inaccurate. Instead, it's a testament to the natural human inclination to track time and the cycles of the moon, which led to the independent development of similar systems across the world.