The architecture of the root system is fundamental to plant productivity. The rate of root growth, the density of lateral roots, and the spatial structure of lateral and adventitious roots determine the developmental plasticity of the root system in response to changes in environmental conditions. One of the genes involved in the regulation of the slope angle of lateral roots is DEEPER ROOTING 1 (DRO1). Its orthologs and paralogs have been identified in rice, Arabidopsis, and several other species. However, nothing is known about the formation of the slope angle of lateral roots in species with the initiation of lateral root primordia within the parental root meristem. To address this knowledge gap, we identified orthologs and paralogs of the DRO1 gene in cucumber (Cucumis sativus) using a phylogenetic analysis of IGT protein family members. Differences in the transcriptional response of CsDRO1, CsDRO1-LIKE1 (CsDRO1L1), and CsDRO1-LIKE2 (CsDRO1L2) to exogenous auxin were analyzed. The results showed that only CsDRO1L1 is auxin-responsive. An analysis of promoter-reporter fusions demonstrated that the CsDRO1, CsDRO1L1, and CsDRO1L2 genes were expressed in the meristem in cell files of the central cylinder, endodermis, and cortex; the three genes displayed different expression patterns in cucumber roots with only partial overlap. A knockout of individual CsDRO1, CsDRO1L1, and CsDRO1L2 genes was performed via CRISPR/Cas9 gene editing. Our study suggests that the knockout of individual genes does not affect the slope angle formation during lateral root primordia development in the cucumber parental root.