Starting from critical RSOS lattice models with appropriate inhomogeneities, we derive two component nonlinear integral equations to describe the finite volume ground state energy of the massive ϕ id , id , adj perturbation of the SU ( 2 ) k × SU ( 2 ) k ′ / SU ( 2 ) k + k ′ coset models. When k ′ → ∞ while the value of k is fixed, the equations correspond to the current–current perturbation of the SU ( 2 ) k WZW model. Then modifying one of the kernel functions of these equations, we propose two component nonlinear integral equations for the fractional supersymmetric sine-Gordon models. The lattice versions of our equations describe the finite size effects in the corresponding lattice models, namely in the critical RSOS ( k , q ) models, in the isotropic higher-spin vertex models, and in the anisotropic higher-spin vertex models. Numerical and analytical checks are also performed to confirm the correctness of our equations. These type of equations make it easier to treat the excited state problem.