It is well-known that the Lorenz ordering, which is widely used to rank the inequality of income, will lead to the ordering of coefficient of variation. This paper finds that these two stochastic orders are equivalent within several common two-parameter families of distributions including the location-scale family, some scale and shape parameter family. Our finding manifests that once the compared life distributions or income distributions belong to a two-parameter family discussed above, rankings by the Lorenz curve and by the coefficient of variation for inequality generate the same order. Furthermore, a simple general sufficient condition without limiting within two-parameter families for this property is provided. These results could extend application of coefficient of variation, which can be regarded as a proxy of Lorenz curve in many cases for an inequality ranking or orderings of life distributions, even if the life has asymmetric heavy-tail distribution.