This note follows a long series of papers of the same author on regular poe-semigroups [see e.g. ibid. 19, 111-121 (1980; Zbl 0434.06015); 23, 85-86 (1981; Zbl 0467.06010); 25, 213-222 (1982; Zbl 0499.06012); 28, 371-372 (1984; Zbl 0534.06006)]. The author establishes a characterization of le-semigroups which are intra-regular and of the intra-regular le-semigroups whose left closed elements are idempotent. As a consequence, a result of \textit{S. Lajos} [Ann. Univ. Sci. Budap., Rolando Eötvös, Sect. Math. 20, 95-97 (1977; Zbl 0324.20063)] is obtained in a slightly improved form.