Cramer-Rao Lower Bound
CRLB is usually used to assess the performance for an unbiased estimator because it is seen as the best variance you can achieve. If I understand your question correctly, you are asking if it is fair to use CRLB to assess the performance for a biased estimator? Well, this may not make much sense because you may come across situations where the biased estimator has better variance than the CRLB! 

For example, Suppose the true value = 0, you can see one estimate is unbiased with large variance but the other has a bias with smaller variance.