Larry won perhaps but not by a lot (8)

I believe the answer is:

narrowly

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'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" .)

I've seen this clue in The Globe and Mail.

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