What is the origin of the word 鬻?
You'd better refer to these links:
https://www.zhihu.com/question/20010669/answer/26173785
https://www.zhihu.com/question/22107477/answer/20311667
https://en.wiktionary.org/wiki/%E9%AC%BB#Etymology
https://en.wiktionary.org/wiki/%F0%A7%B6%A0#Chinese

The word {congee} was first denoted by  (here 毓 denotes its pronunciation and 䰜 stands for cooking utensils) and later the character developed into 鬻(鬻≠粥+鬲，鬻=米+䰜). Finally it was simplified to 粥.

Both 粥 and 鬻 could be used to denote the word {sell}. As dROOOze pointed out,
this use is nothing but a phonetic loan for .  stills exists as a phonetic complement in many characters like 續贖讀櫝 (its glyph form becomes resembling 賣mài but they are etymologically unrelated).


As the history developed the usage of 鬻 to mean {sell} was fixed and 粥 became only used to mean {congee}.

The use of 鬻 to mean {sell} is seen as traditional Chinese today and hence only appears in idiomatic uses.

Examples in ancient Chinese:
楚人有鬻楯與矛者。 There was a person in Chu state who was selling shields and lances.
我世世為洴澼絖，不過數金；今一朝而鬻技百金，請與之。We have been bleaching cocoon-silk for generations, and have only gained a little money. Now in one morning (=at once, immediately) we can sell [to this man] our art (the way to make a salve which kept the hands from getting chapped) for a hundred ounces - let me give (sell the art) to him(=let him have it).