There are a lot of sci-fi plots where mutagens, especially radiation, cause some organism to evolve at an accelerated rate. Obviously evolution does not occur within a single organism and most of the authors behind these works are more concerned with finding a justification for a desired plot rather than adhering to known science. Nonetheless, I'm curious to know if there is any well-known case where such a scenario is true. (To get one obvious reply out of the way, all evolution that we've observed on Earth occurs in the presence of the background radiation experienced on Earth. Also, although mutagens by definition increase the rate of mutation, those mutations can of course be harmful, so the question is whether the effective "rate of evolution" can be increased rather than the rate of mutation.)
Is there any well-known case where introducing mutagens can increase the "rate of evolution" in an experimental evolution study?
By "rate of evolution", I'm informally referring to either the amount of time or the number of generations that pass before some beneficial mutation occurs and is selected for. For example, in the E. Coli strains from Lenski's E. coli evolution experiments, are there any known cases where a mutagen reduces the amount of time or the number of generations required for a non-citrate-metabolizing E. coli strain to acquire the ability to metabolize citrate?