In the Hobbit I think it says that the elves of Mirkwood got a lot of their food from trade with the men of Laketown.
As to farming, I think I have seen somewhere that their were some elves who did farm. Also, the elves I think only used Lembas as a food source when they were travelling, not as general day to day food.
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His sword was long his lance was keen
His shining helm afar was seen
The countless stars of heavens field
Were mirrored in his silver shield
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