Drink that could make lad emotional, losing head (11)
I believe the answer is:
amontillado
'drink' is the definition.
(amontillado is a kind of drink)
'could make lad emotional losing head' is the wordplay.
'could make' indicates an anagram.
'losing head' means to remove the first letter.
'emotional' with its initial letter removed is 'motional'.
'lad'+'motional'='ladmotional'
'ladmotional' with letters rearranged gives 'AMONTILLADO'.
'that' acts as a link.
(Other definitions for amontillado that I've seen before include "Medium-dry sherry" , "Drink" , "Type of sherry" , "Pale sherry" , "booze" .)