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."
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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..."
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Quite simply this is another way of saying "Do me favour". However this version tends to be used by people who live in and or frequent London, England.
Often it is used to express disbelief in what someone is saying .
#1 Do me a lemon, and give me a lift to the pub.
#2 Do me a lemon, there's no way he said that you absolute muppet.