How to interface with LCD display - HYeLCD, HC20216NYU
That lcd is a typical dime a dozen, hd44780 or ks0066 compatible Character LCD display. The HD44780 is a standard parallel input display controller, with well documented information, and 99 out of 100 character lcd displays will use the same protocol. Heck, even some serial, i2c, and spi character displays are really HD44780 displays with a secondary chip (often called a backpack) acting as a middleman.

And Yes, that Propeller object you link to will work for it. In fact, here is more: http://obex.parallax.com/search/HD44780