Lunar Sabbath/Shabbat Questions

Hey everyone! I am not jewish, but I work with someone who claims to be of the “Israelite faith//sub Christian religion”. I apologize if I get some terminology wrong, but they also could not explain it very well.

I understand the basic rules of “light no fire” and “do no work or travel” on such days that are separated as rest. However, she is claiming that based on the moon phases she cannot work during each week. For example, this next week it would be Wednesday, and then after a few weeks it shifts to Thursday and so on as the lunar cycle persist. From what I could find online, it doesn’t seem to align with any mainstream Jewish faiths. I want to try and better understand it, so I can be accommodating.

I want to express that I mean no harm with this line of inquiry, but if anyone could point to some sources or explanation of any groups that still follow it that would be appreciated.

She used explicitly the words of “isrealite faith”, so I figure it has to be some Jewish dysphoria. She won’t give me anymore specifics such as the name of her group or anything, so I can kind of working in the blind and do not want to offend. Thank you in advance for anyone that can help me better understand my coworker!