Among the various kinds:
lattuga bionda or liscia: leaf lettuce, butterhead
lattuga gentile: batavia
lattuga romana: cos, or romaine
lattuga riccia or endivia: curly endive. They have a unique, slender-leaved variety of this called romanesca.
lattughella: soncino, lamb's lettuce
iceberg is iceberg, though there is a native south Italian version called incappucciata.
lingua di canarino: oak leaf lettuce
Note that lattughe can also be fried pastries; see chiacchiere.
In Liguria, lattuga ripiena alla genovese is a popular if finicky-to-make starter: the lettuce leaves are parboiled and filled with minced beef, onion, breadcrumbs, then cooked in a tomato sauce.