We report the detailed analysis of specific heat [CP(T)] and ac-susceptibility for magnetically frustrated Sr2−xLaxCoNbO6 (x = 0-1) double perovskites to understand low temperature complex magnetic interactions and their evolution with x. Interestingly, the observed Schottky anomaly in the x 0.4 samples shifts gradually towards higher temperature with magnetic field as well as x, and the analysis reveal the persistence of the discrete energy states in these samples resulting from the spin-orbit coupling and octahedral distortion. Moreover, the extracted values of Landé gfactor indicate the existence of high-spin state Co 3+ ions close to non-magnetic low-spin state. The specific heat data show the λ-type anomaly for the x 0.6 samples due to evolution of the long range antiferromagnetic ordering. Our analysis of low temperature CP(T) data for the x 0.6 samples demonstrate the 3D isotropic Heisenberg antiferromagnetic (AFM) interactions and the temperature induced second order AFM-paramagnetic phase transition. More interestingly, we demonstrate the presence of the free Co 2+ like Kramers doublet ground state in the x =1 sample. Further, the ac susceptibility and time evolution of the magnetization data reveal the low temperature cluster-glass like behavior in the x = 0-0.4 samples, where spin-spin correlation strength decreases with x.