sell, deal in, rice gruel
鬻 centers on selling or dealing in goods, with a secondary, likely older meaning of rice gruel. The two senses may be historically connected through the idea of trading in foodstuffs, but they are distinct in modern usage.
鬻 is a complex character whose exact historical development is uncertain. It appears to combine 䰜 (a variant of 鬲, a cauldron) with 米 (rice), suggesting the original meaning of rice gruel. The 'sell' meaning may have arisen from phonetic borrowing or semantic extension, but the connection is not clearly established.
Inside a large cauldron (the lower part resembling 鬲), rice (米) is being cooked into gruel. Picture someone selling this steaming rice gruel from the cauldron at a market.
For イク, imagine a merchant shouting 'Eek! I cook rice gruel to sell!' The 'eek' sound (イク) ties the selling meaning to the reading.