* משורר לירי (mishorrer liri): This is the most straightforward translation. משורר (mishorrer) means "poet," and לירי (liri) is the Hebrew word for "lyric" (borrowed from English/Greek). This is a perfectly acceptable and commonly understood term.
* משורר שירה לירִית (mishorrer shira lirit): This translates to "poet of lyric poetry." It's more verbose but emphasizes the *type* of poetry written. שירה (shira) means "poetry."
The best choice depends on the context. For general use, משורר לירי (mishorrer liri) is sufficient and clear.