This paper considers some properties of a two-sample test, suggested by Lehmann , against general alternatives. Alternative expressions are given for the test statistic; a general formula for the variance is derived and evaluated for the null case; the expectation is obtained in certain nonnull cases; and the exact distributions in the null case are tabulated for some small samples.
R. M. Sundrum. "On Lehmann's Two-Sample Test." Ann. Math. Statist. 25 (1) 139 - 145, March, 1954. https://doi.org/10.1214/aoms/1177728853