This paper derives the Cramer-Rao lower bound (CRLB) on estimates of phase in long baseline interferometry (LBI) based localization systems. LBI localization is a classical method for finding the location of a non-cooperative emitter by estimating the phase difference between received signals by two sensors spatially separated on a single platform. In this paper, we derive the CRLB for phase difference in LBI-based systems by modelling the received signal as a deterministic unknown; that is, its samples are considered as nuisance parameters to be estimated. Consequently, the CRLB computations become much more complicated in this case. Finally, we provide the discussion for our results.