Girl awfully lonely, having lost love (5)
I believe the answer is:
nelly
'girl' is the definition.
'awfully lonely having lost love' is the wordplay.
'awfully' indicates an anagram.
'having lost' is a deletion indicator.
'love' becomes 'o' (In tennis, 'love' means 'zero').
'lonely' with 'o' taken out is 'lnely'.
'lnely' anagrammed gives 'NELLY'.
(Other definitions for nelly that I've seen before include "Let not poor - starve (Charles II)" , "Silly person" , "Life" , "Girl" , "Fool" .)