Playford Edition:

‘Lusty Gallant’ can be located in the  edition of The [English] Dancing Master, (1651). 

Documentation Between 1603-1651:

  Information to follow.

Documentation prior to 1603:

Thomas Nashe mentions the Lusty Gallant in Terrors of the Night (1594), where he says:

•  “After they all danced Lusty Gallant…” ⁽¹⁾

The ‘Lusty Gallant’ is mentioned in Nicholas Breton’s Works of a Young Wit, (1577):

• “And then you know, the youth must needs go dance,
  First galliards -- then larousse, and heidegy --
  Old Lusty Gallant -- All the flowers of the Broom.
  And then a hall, for dancers must have room...
  And to it then: with set, and turn about,
  Change sides, and cross, and mince it like a hawk;
  Backwards and forwards, take hands then, in and out;
  And, now and then, a little wholesome talk,
  That none could here, close rowned in the ear.'” ⁽²⁾

Musical History:

The tune for 'Lustie Gallant' is mentioned in A Handfull of Pleasant Delites as the tune that accompanies "A proper song, Intituled: Fain wold I have a pretie thing to give unto my Ladie. ⁽³⁾

The tune for the Lusty Gallant survives in several sources:

• Dallis Lute Book (c: 1583)
   
• Marsh Lute Book (c: 1595)
   
• Trinity College MS 408/2 (c: 1605)