One of the standard Western musical modes. The name had one meaning to the ancient Greeks, then was given a different meaning by medieval theorists who misunderstood the Greek treatises.
It is unclear exactly what type of scale was meant by Aristotle and the other ancient Greek authors. Boethius, in his description of ancient Greek usage, stated that the lydian mode was a musical scale which would be represented in modern form as the octave-species from C to C, in ascending order thus ("t" = whole-tone, "s" = semitone):
C D E F G A B C t t s t t t s
Note that this example illustrates the diatonic genus -- the various ancient Greek modes had variant interval structures, depending on the genus and shade.
In ecclesiastical and modern usage, dating from the incorrect application of Boethius's names to the system of church modes in the Alia Musica (c.870), the lydian mode is the diatonic octave-species from F to F, in ascending order thus ("t" = whole-tone, "s" = semitone):
F G A B C D E F t t t s t t s