Amazing thing (4)
'amazing thing' is the definition.
(I've seen this in another clue)
This is all the clue.
(Other definitions for lulu that I've seen before include "Glaswegian 60s pop singer" , "Outstanding person; singer" , "Berg opera; outstanding thing (colloq.)" , "Attractive girl" , "Outstanding example of its kind - Alban Berg opera - Scottish pop singer, b. 1948" .)
(Other definitions for beaut that I've seen before include "16 down's fine or attractive example of something" , "fine thing" , "cracker" .)