The phrase "work into a rich lather" typically refers to the process of creating a foamy, soapy texture while washing oneself or a particular item. Some synonyms for this phrase could include "gently agitate," "work up a good froth," "create a creamy emulsion," or "whip into a creamy foam." Additionally, one could describe this process with more descriptive language, such as saying "massage the soap to create a luxurious foam" or "apply pressure to lather up the shampoo." Ultimately, the goal is to create a rich, velvety texture that effectively cleanses and refreshes whatever is being washed.