The Monolith is seemingly made entirely out of grey rock. Its "blade" takes the form of a moai in profile, while its counterweight is a flat section of rock that juts out from the back of the moai's head. The Monolith may be a reference to the fact Lexaeus tends to be "stone-faced".
A monolith is a large block of stone used for sculpture or architecture. It can also refer to anything massive and unmovable. "Rockhead" clearly refers to the weapon's appearance, a stone moai. The Moai also serve as recurring easter eggs within the Final Fantasy series.
The Monolith's ground combo starts with a single-handed downward slash, followed by a diagonal upward slash, and ends with a powerful, two-handed downward slash.
The aerial combo consists of a two-handed, upward slash, followed by a downward slam.