You can start from one of a lily: white all over, with nothing else on it at all. What makes that image useful is not the colour but the absence — one would show immediately, so a surface like that is proof that nothing has landed on it. Every use of this word is a claim that something is clear in that way: a piece of cloth, a person's record, or the make-up of a group.
可以先想一片百合花瓣：整片都是白的，上面什麼都沒有。真正有用的不是那個顏色，而是那份「空無一物」。因為一粒灰塵掉上去就會被看見，所以這樣一面白，本身就是「什麼都沒沾到」的證明。這個字的每個用法，都是在主張某個東西乾淨到這種程度：一塊布、一個人的紀錄，或是一群人的組成。
From the word’s history
The evidence packet gives lily-white as Middle English liliwhite, that is lily plus white. The flower is in the word from the start, which is why the word has always said more than the colour alone.
供給的資料寫明：lily-white 來自中古英語的 liliwhite，就是 lily（百合）加 white（白）。百合從一開始就在這個字裡面，所以它講的從來不只是顏色，還有那份乾淨到沒有雜質的樣子。
Wiktionary, "lily-white"
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