Larry won perhaps but not by a lot (8)
I believe the answer is:
narrowly
'not by a lot' is the definition.
I can't judge whether this definition defines the answer.
'larry won perhaps' is the wordplay.
'perhaps' indicates an anagram.
'larry'+'won'='larrywon'
'larrywon' with letters rearranged gives 'NARROWLY'.
'but' acts as a link.
Can you help me to learn more?
(Other definitions for narrowly that I've seen before include "By the skin of one's teeth" , "Adverb meaning with little margin - sounds strait" , "By only a small margin" , "Closely" .)