How to lock layers on the timeline in FCPX?

There no way to lock a layer in FCP, probably because there are no actual tracks in the software.

A few thoughts:

1) If you are editing to music, put the music in the primary storyline, and connect video to it. This way the music is not affected when you make cuts in the video.

2) If you are editing something that was shot with two cameras, you should learn how to use multicam clips.

A multicam clip will have the material from both cameras in separate Angles, and you cut from one to the other as simply as pressing 1, or 2, on your keyboard.

Here is a good and easy introduction to using multicam clips:

https://www.youtube.com/watch?v=X5baUmK8noc

There is no way to lock “tracks.” There are no tracks. If you’re using multicam editing, the simplest way is to detach the audio so it’s only connect at one point. The camera switch will then not cut the audio.

I am cutting clips on a two camera edit, and have music under

As Tom says, it's a good idea to separate the video and audio into separate clips and place them on the timeline. You can separate the sound by pressing shift+control+S.