By lot is a phrase commonly used to describe a method of selecting or deciding through random chance. However, there are several synonyms that can be used interchangeably with this phrase. One of the most commonly used synonyms is "by chance", which connotes the element of unpredictability in the selection process. Other synonyms include "by luck", "by fate", and "randomly". Additionally, the phrase "by drawing lots" can be used as a more formal way of referring to the same process. Regardless of the term used, the idea remains the same: a decision is made without any preconceived notion or bias.