Let \(\alpha \in (0,n)\) . In this article, the authors study the Lorentz properties of the fractional commutator \([b,I_\alpha ]\) which is generated by the Riesz potential and a symbol b. Moreover, the equivalent characterizations of the boundedness of \([b, I_{\alpha }]\) on Lorentz spaces in terms of \(b \in \textrm{BMO}_{\beta _{1}}(\mathbb {R}^n)\) , and the Lorentz compactness characterizations via \(b \in \textrm{CMO}_{\beta _{2}}(\mathbb {R}^n)\) are also established, where \(\beta _1\in [0,1]\) , \(\beta _2\in [0,1)\) , and \(\alpha +\beta _i\in (0,n)\) for \(i = 1,2\) .
