It may be either fretted or unfretted. Lutes are fascinating string instruments with a rich history The lute is a stringed musical instrument plucked with the fingers or a plectrum (pick).
lute (hazbin hotel) drawn by rukiadaichi | Danbooru
Lute, in music, any plucked or bowed chordophone whose strings are parallel to its belly, or soundboard, and run along a distinct neck or pole
In this sense, instruments such as the indian sitar are classified as lutes.
The lute derives its name, as well as its distinctive shape, from the arabic 'ud, an instrument which is vey much at the heart of arabic musical life to this day.