This paper studies the joint digital self-interference (SI) cancellation and data detection in an orthogonal-frequency-division-multiplexing (OFDM) full-duplex (FD) system, considering the effect of phase noise introduced by the oscillators at both the local transmitter and receiver. In particular, an universal iterative two-stage joint SI cancellation and data detection framework is considered and its performance bound independent of any specific estimation and detection methods is derived. First, the channel and phase noise estimation mean square error (MSE) lower bounds in each iteration are derived by analyzing the Fisher information of the received signal. Then, by substituting the derived MSE lower bound into the SINR expression, which is related to the channel and phase noise estimation MSE, the SINR upper bound in each iteration is computed. Finally, by exploiting the SINR upper bound and the transition information of the detection errors between two adjacent iterations, the universal bit error rate (BER) lower bound for data detection is derived.