The Lapis Dragon can be bred through combining a Sandstorm Dragon with a Thunder Dragon at the Breeding Cave or Epic Breeding Island. It cannot be bred with any other dragon, including another Lapis Dragon. You can also purchase the Lapis Dragon for 1,500 gems.
For a short period of time, the Lapis Dragon was available for a reduced price of 150 gems. This deal has been expired since March 10, 2014, though. The wizard who spent most of his life studying the Lapis Dragon, Pablue Pickaxe, heavily references the real-life artist Pablo Picasso. This includes both men having similar names and an obsession with blue things (Picasso is famous for his Blue Period in which he mostly painted in shades of blue and green). The design of the Lapis Dragon itself is inspired by Egyptian culture, with its head shaped similarly to a Pharaoh's headdress and the gold detailing on its wings and tail similar to Egyptian heiroglyphics and religious symbols. Lapis lazuli, the gemstone the Lapis Dragon was named after, is noted for its striking blue color, and is found in Egyptian funerary objects of pharaohs as well as the expensive clothing dye used in the Middle Ages to give off the color known as royal blue.