Abstract: In this paper we derive a new class of time inconsistent dynamic coherent risk measures, allowing the interest rates involved to be random, which extends and modifies the results on risk measures in Appl. Anal. 86 (2007), 1429–1442. Since in this procedure one important mathematical tool is a kind of backward stochastic Volterra integral equations (BSVIEs in short) with stochastic Lipschitz coefficients, this paper firstly is devoted to develop the existence and uniqueness theory for the corresponding BSVIEs, which not only generalizes the results in Stoch. Proc. Appl. 116 (2006), 779–795; Appl. Anal. 86 (2007), 1429–1442; Probab. Theory Related Fields 142 (2008), 21–77; but also simplifies considerably the related arguments there.