What is lyric poetry?
Lyric poetry is a formal type of poetry which reveals the poet's personal emotions or feelings, state of mind or perceptions. It is usually written in the first person.
Edna St. Vincent Millay's "Love is Not Love at All" is a good example of lyric poetry:
Love is not all: it is not meat nor drink
Nor slumber nor a roof against the rain;
Nor yet a floating spar to men that sink
And rise and sink and rise and sink again;
Love can not fill the thickened lung with breath,
Nor clean the blood, nor set the fractured bone;
Yet many a man is making friends with death
Even as I speak, for lack of love alone.
It well may be that in a difficult hour,
Pinned down by pain and moaning for release,
Or nagged by want past resolution's power,
I might be driven to sell your love for peace,
Or trade the memory of this night for food.
It well may be. I do not think I would.
Notice how the highlighted portions indicate the poet's thoughts on love.
Some other examples would include William Wordsworth's "I Wandered Lonely as a Cloud", and Shakespearean sonnets.
Hope this helps :)