I'd say that Lyric poetry refers to a usually short poem that expresses personal feelings, which may or may not be set to music.(Aristotle, in Poetics, contrasted lyric poetry with drama and epic poetry. An example would be a poem that expresses feelings and may be a song that could be performed to an audience)
Free verse - also known as vers libre - is a term describing various styles of poetry that are written without using strict meter or rhyme, but still recognizable as poetry by virtue of complex patterns of one sort or another that readers will perceive to be part of a coherent whole. However, much like blank verse poetry, it has been suggested that free verse poetry be recategroized simply as another type of literary composition since, in contrast to literally ever other type of traditional poetry, it doesn't rhyme.