"Fra Lippo Lippi" shouldn't pose too much trouble for readers. It's written in a conversational manner, which definitely helps speed things along. It reads like a friend (albeit one that's tossed back a few too many brewskis) giving you the scoop.
Where the poem can get a little tricky is in its allusions. You'll have to be on your toes looking up the references to saints (e.g., John the Baptist vs. St. John), as well as some of the locations that Lippo mentions (Sant'Ambrogio and the St. Laurence, for instance). There are also a few archaic words that Browning uses to mimic what a typical fifteenth-century monk might sound like. So, keep a dictionary handy for things like "kirtle," "zooks," and "cullion."