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1.
Means literally 'do me a favour'. The lemon part is Cockney rhyming slang, and is short for 'lemon flavour', so in other words it's really "do me a lemon flavour"

The usage is mostly to reject an offer or behaviour of some kind, due to its being undesirable in some way (as opposed to actually asking for a specific favour).
"Do you want to buy my iPod for 100 quid?"
"Do me a lemon. I could get one on ebay for 50."
by NoMoreSecrets December 05, 2007
 
2.
Rare but recorded London phrase for 'Do me a favour'. Totally mystery origin, unless you know the answer.
"Oi Trev, you're not saying you need my motor again, do me a lemon..."
by David from Kingsbury April 13, 2006