Should composer.lock be committed to version control?

For applications/projects: Definitely yes.

The composer documentation states on this (with emphasis):

Commit your application's composer.lock (along with composer.json) into version control.

Like @meza said: You should commit the lock file so you and your collaborators are working on the same set of versions and prevent you from sayings like "But it worked on my computer". ;-)

For libraries: Probably not.

The composer documentation notes on this matter:

Note: For libraries it is not necessarily recommended to commit the lock file (...)

And states here:

For your library you may commit the composer.lock file if you want to. This can help your team to always test against the same dependency versions. However, this lock file will not have any effect on other projects that depend on it. It only has an effect on the main project.

For libraries I agree with @Josh Johnson's answer.

If you update your libs, you want to commit the lockfile too. It basically states that your project is locked to those specific versions of the libs you are using.

If you commit your changes, and someone pulls your code and updates the dependencies, the lockfile should be unmodified. If it is modified, it means that you have a new version of something.

Having it in the repository assures you that each developer is using the same versions.