Lateral pipe simply refers to the pipes which consumers would use in their gardens or backyards as the "final piping" for your irrigation system. LDPE and MDPE on the other hand are specific types of material, determined by their density, thus the names Low Density Polyethylene and Medium Density Polyethylene.
For most backyard and residential applications, a Lateral pipe will suffice. However, for systems with drip or many sprinklers, then LDPE may be required. For more commercial applications MDPE or even HDPE may be required.