What makes a L-cut or J-cut work is the combination of dialogue and imagery.
For an L-cut, the dialogue of the entertainer continues as the camera cuts to another video.
For a J-cut, the dialogue plays while we see environmental videos (B-roll), but then cuts to the source of the dialogue.
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J-cuts and L-cuts are similar, but different.
By definition, J-cuts are scene transitions where the audio of the next scene precedes the picture change.
In an L-cut, the audio carries over from the previous scene into the following one, despite visual changes.
The visual cut itself should remain the same, however audio is either brought in early from the next clip (a J-cut) or the audio from the previous clips stays under the new clip (a L-cut).