Lillian definitively has 3 Ls. That is per Google Translate, which is the origin of "lillian" to begin with. Lillian is Google's English translation of Japanese pronunciation of an English phrase. (Ever play "telephone" as a kid? What comes back to you is never even close to what you started with.)

Lillian started out as "lily yarn" which was called that because the shape the cord takes as you are weaving it looked like the shape of a lily flower. (Young Japanese girls all used to have a toy with which they could weave the cord.) When "lily yarn" is written in Japanese, it is written as リリアン. Japanese has no "L" sound and no "rn" sound, so it is written as ree-ree-yah-nn. Google is smart(?) enough to know that reereeyahnn is meaningless in english, but that "lillian" is written as リリアン, so リリアン comes out as lillian when run through Google Translate.

Early on, I knew that to be precise "lillian" should be translated as lily yarn, but it was just so much easier to leave it as lillian and not have to explain why when people looked at Japanese web sites it was referred to as lillian and I was writing about lily yarn. So, it's all my fault and I take full responsibility.