Should Cargo.lock be committed when the crate is both a rust library and an executable?

Yes, crates that depend on your library will ignore your Cargo.lock. The Cargo FAQ provides more details:

Why do binaries have Cargo.lock in version control, but not libraries?

The purpose of a Cargo.lock is to describe the state of the world at the time
of a successful build. It is then used to provide deterministic builds across
whatever machine is building the package by ensuring that the exact same
dependencies are being compiled.

This property is most desirable from applications and packages which are at the
very end of the dependency chain (binaries). As a result, it is recommended that
all binaries check in their Cargo.lock.

For libraries the situation is somewhat different. A library is not only used by
the library developers, but also any downstream consumers of the library. Users
dependent on the library will not inspect the library’s Cargo.lock (even if it
exists). This is precisely because a library should not be deterministically
recompiled for all users of the library.

If a library ends up being used transitively by several dependencies, it’s
likely that just a single copy of the library is desired (based on semver
compatibility). If Cargo used all of the dependencies’ Cargo.lock files,
then multiple copies of the library could be used, and perhaps even a version
conflict.

In other words, libraries specify semver requirements for their dependencies but
cannot see the full picture. Only end products like binaries have a full
picture to decide what versions of dependencies should be used.