That is the problem with anthias in general, but worse with an aggressive fish like the Lyretail. I was advised to try to get the smallest females possible in the hope that they are all truly female and not changing. It is good to hear that yours leave everyone else alone.
You'd think 420 would be huge, and it's not small (90 x 36 x 30), but after putting in 4 tangs and a bunch or wrasses, I think adding a ton of fish would cause problems and look too crowded. Plus, I don't want any fish that would even possibly eat coral, so the list of eligible fish dwindles ... thus why I'm looking at anthias.