As you're interested in testing the behavior of the Application Service itself, there's no need to turn it into an integration test with complicated setups going against a real database. You're not interested in testing the low-level details, so most of the time, a unit test will be enough:

class SignUpUserServiceTest extends \PHPUnit_Framework_TestCase
{
    /**
     * @var \Lw\Domain\Model\User\UserRepository
     */
    private $userRepository;

    /**
     * @var SignUpUserService
     */
    private $signUpUserService;

    public function setUp()
    {
        $this->userRepository = new InMemoryUserRepository();
        $this->signUpUserService = new SignUpUserService(
            $this->userRepository
        );
    }

    /**
     * @test
     * @expectedException   
     *     \Lw\Domain\Model\User\UserAlreadyExistsException
     */
    public function alreadyExistingEmailShouldThrowAnException()
    {
        $this->executeSignUp();
  ...