In that example they should still rank for "lyrics.com" which would be the BRAND term.

Google actually have done an EMD update to devalue sites trying to rank for generics using a generic domain.

As you can see using Google Adword Keyword Planner[1] for all locations in English the average searches are:

Lyrics - 1.2M avg. searches/month

Lyrics.com - 110k avg. searches/month

[1] https://adwords.google.com/ko/KeywordPlanner/