An interesting class of integrable deformations of 2-dimensional quantum field theories are $\overline TT$ deformations. These deformations are well defined in any translationally invariant quantum field theory, including those without Lorentz invariance, such as Warped CFTs. Warped CFTs are the boundary dual to Warped AdS spacetimes, which are solutions to lower spin gravity. By adapting the deformed boundary conditions recently discussed in the context of holographic dual $\overline TT$ deformed CFTs, we investigate how $\overline TT$ deforming a Warped CFT affects its bulk dual. We also explore some non-holographic examples of $\overline TT$ deformed WCFTs.