This one's easy peasy. The title, "Fra Lippo Lippi," is the name of the main speaker of the poem. Brother Lippo was a real-life artist from Florence, Italy, who is commonly thought to be the first realistic painter.
At the time he was painting (around the late thirteenth through early fourteenth centuries), this was a big deal and was considered groundbreaking for many of the reasons Lippo expresses in the poem. The Church wanted a say in art to make sure that it focused on suitably spiritual things, and not just the human body or depictions of real life.
Fun fact: Browning came up with the idea of writing in the voice of Lippo after he read Giorgio Vasari's The Lives of the Artists, a collection of biographies about Renaissance painters.