A ballad is a poem that tells a story of romance or adventure. Most of them are written in four to six line stanzas, and they have a definite rhyming pattern. Many times they have refrains, which are regularly repeated lines or stanzas. They can be sung and usually have characters in them. An example of a ballad would be "The Highwayman" by Alfred Noyes. A dashing robber falls in love with Bess, the innkeeper's daughter. Unfortunately, due to a jealous suitor, Bess ends up killing herself to save her lover, and then he returns to be killed by the soldiers. Another example is "The Ballad of Birmingham" written about the true event of the bombing of a church in Birmingham in which four little girls were killed. See the reference link below to read more about it.
A lyric poem has a single speaker and usually expresses feeling or emotion. It is also highly musical. The original lyric poems of Aristotle's time were accompanied by a lyre, a harplike instrument played by the ancient Greeks. Lyric poems do not have to rhyme, however. They do NOT tell a story. An example of this would be Lord Byron's "Maid of Athens, Ere We Part". See the link below to view the poem. It professes his love for this maid in Athens. It has one speaker and expresses his feelings of love.