Convert WordPress calendar from Gregorian to Lunar

Hello.

I’m developing a website that sells products based on Lunar calendar using Woocommerce and Woocommerce subscription.

Problem 1:
Subscribers are supposed to pay on the first day of every month of Lunar calendar.
However, since WordPress system is under Gregorian calendar, the first day of every month for Gregorian’s doesn’t correspond to Lunar’s first day.

(For 2018)
March 1 in Lunar is April 16 in Gregorian.
April 1 in Lunar is May 15 in Gregorian.

Problem 2:
The subscription products are also determine by the date the customer signed up.
For example, some product only shipped in Lunar’s August.
If the customer sign up on Gregorian’s September 1, the system assume August has passed, but in reality Lunar’s August actually starts from Gregorian’s September 10.

I hope the explanation isn’t too confusing, with two calendars jumping here and there.

Anyway, I’ve found a library in php for the conversion:
https://github.com/overtrue/chinese-calendar

I’m capable of coding in php/mysql and any language related to WordPress.

So is it possible, and if so how do I convert the system datetime into lunar calendar?