To make an L-Cut, you go into the Precision Editor. To do that, click on the clip after the transition, and choose Precision Editor from the tools menu popup. The Precision Editor opens at the bottom of the iMovie workspace. Click the show/hide audio waveforms button to see the audio track underneath the video. To make an L-Cut, simply click-and-drag the blue vertical bar in the audio channel (see below.)
Where I got hung up was, I was trying to add an L-cut to an edit with a transition. Things change a little because there are now two blue bars (indicating the beginning and ending of the transition.) You don't click on one of the blue bars, you click in the space between the blue bars and then drag. I spent ages trying to drag those damn blue bars!
This short video shows you how to do it.