The Director's Cut (not actually a true director's cut, but a marketing promotion by Warner Bros.) features seven minutes of additional footage. In a new trailer scene, Riggs smashes his TV with a beer bottle; later he buys a new one. Murtaugh, before partnering with Riggs, goes to practice at the firing range. Riggs, before the dope shoot out, answers a call in a school yard with a sniper. Riggs walks out into the line of fire and kills the sniper, emptying his clip into him. Riggs, after leaving Murtaugh's house, goes out to solicit a prostitute. The aftermath is not shown, but Riggs says he wants to take her home to watch The Stooges with him; for this he pays her $100.
All versions of "Lethal Weapon" released in Germany before the Director's Cut had a rating FSK 16, and were all slightly cut. The Director's Cut of LW 1 released in 1998 is uncut, but also got an FSK 16 rating.
The British TV version cut out most of the electric shower torture scene whereas the USA TV version left in the torture but cut out the "should marijuana be legalized" argument between Murtaugh and his daughter.