Not much difference in the audio, but there are other factors to consider: longer Director's Cut, "Making Of" featurette, and director's audio commentary, all of which make this purchase a no-brainer if you haven't already bought the previous bare-bones flipper from Warner.
None of the first three Lethal films have audio commentary tracks.
The first three Lethals were re-issued as the director's cuts with a new dts English sound option.
Lethal Weapon 2 had a trailer and stunt featurette on the original disc, this was carried over to the re-release. But Lethal 2 was presented in letterbox in the original release. The director's cut of Lethal 2 is presented in anamorphic widescreen.
Lethal Weapon - Director's Cut is definitely a must purchase. It includes some great character development and adds a scene that explains the dialogue in the parking garage. This scene show how far down Martin Riggs has gone since the loss of his wife.