You can include it, but

- either you use chroot, proot or similar to make /lib path contain your executable’s loader

- or you hardcode different loader path into your executable

Both are difficult for an end user.

This isn't that hard (that's not to say this is easy, it is tricky). Your executable should be a statically linked stub loader with an awful lot of data, the stub loader dynamically links your real executable (and libraries, including libc) from the data and runs it.