This work presents the second paper of the CoreLumen Gravity series. Starting from the modified Einstein equations derived inCoreLumen Gravity I, we develop the linear perturbation theoryof condensate gravity around a homogeneous cosmological background. The vacuum is modeled as a phase condensate described by theorder parameter Ψ = ρ e^{iθ}. Scalar perturbations of the metric and condensate fields areorganized into amplitude and phase fluctuations. In the regimerelevant for large-scale structure observations the heavyamplitude mode decouples, leaving the condensate phase modeas the dominant mediator of gravitational response. The resulting modifications of the gravitational sector can beexpressed through the effective response functions μ(k,z) and Σ(k,z), which respectively govern matter clustering and weak-lensingobservables. In the quasi-static regime the response functions take thescreened form μ(k,z) = 1 + β₁ k² / (k² + m_θ² a²)Σ(k,z) = 1 + β₂ k² / (k² + m_θ² a²) which interpolate between a large-scale general-relativisticlimit and a small-scale modified response. This work establishes the perturbative interface between thecovariant condensate gravity framework and the response-levelobservational language used in the CoreLumen Stage and COSprograms.