Apparently the crossguard lightsaber design was part of the Jedi tradition. In Star Wars Rebels, Ezra and his friends entered the Great Scourge site on Malachor and discovered such a weapon. Perhaps Luke found the design after the fall of the Empire and shared the information with Kylo.
The Great Scourge of Malachor was first referenced in the 2015
reference book Star Wars: The Force Awakens: The Visual Dictionary,
which stated that the crossguard design of Kylo Ren's lightsaber was
an ancient one that dated back thousands of years to the Great Scourge
of Malachor. The book's author, Lucasfilm Story Group creative
executive Pablo Hidalgo, added the reference to the book to connect it
with the battle that was ultimately referenced in "Twilight of the
Apprentice," the second season finale of the animated television
series Star Wars Rebels.
On the other hand, however, it is not certain Kylo constructed the lightsaber himself...