Can Levitate Move Horizontally?

It cannot. Again, there is no inertial movement unless you are in zero gravity environments, and the spell doesn't allow horizontal movements either.

Can you move with levitate?

Instead, Levitate does exactly what it says it does: it allows you to move up to 20 feet in either direction "as part of your move."

How does levitate work DND?

One creature or object of your choice that you can see within range rises vertically, up to 20 feet, and remains suspended there for the Duration. ... The target can move only by pushing or pulling against a fixed object or surface within reach (such as a wall or a ceiling), which allows it to move as if it were climbing.