Ah, the answer is:
If you say farewell twice
You'll find this one under
'Farewell twice' is Bye bye. 'Under' that (as in, after it) you can put the word "Birdie' to make a film title and expression: "Bye Bye Birdie'. 'Birdie' is also a golfing term for a ball holed 'one under par' (i.e. in one shot fewer than the difficulty of the hole might suggest).
Watch it real close
Then lightning - no thunder
If you are 'watching the birdie' you are having your picture taken by a photographer (it's something the photographer might commonly say to ensure you are looking at the camera). Then he/she presses the flash ('lightning') and your portrait is immortalised in film!
Furthermore, this satisfies the title and first hint since:
Birdie is a girl's name (albeit perhaps more common among older generations).