Depending on whether it has a smoothbore or rifled barrel, then by the current production it is a Model 1 or 2. It used to be the case that the Model 1 was smoothbore, fixed sights, and the 2 was rifled, adjustable sights - the same as the Model 3.
Originally, the 1 and 2 also had an open, exposed front sight; the different design of barrel casting with a hood seems to have been introduced in about 1983 or so with the large-gripped Model 3.
http://www.record-firearms.de/en/pro...dell-lp-1.html
Iain