Inspired by the newly observed Lambda _b(6072) structure, we investigate its strong decay behaviors under various assignments within the ^3P_0 model. Compared with the mass and total decay width, our results suggest that the Lambda _b(6072) can be regarded as the lowest rho -mode excitation in Lambda _b family. Then, the strong decays of rho -mode nonstrange partners for the Lambda _b(6072) are calculated. It is found that the J^P=5/2^-Lambda _b and Lambda _c states are relatively narrow, and mainly decay into the Sigma _b^{(*)} pi and Sigma _c^{(*)} pi final states, respectively. These two states have good potentials to be observed in future experiments, which may help us to distinguish the three-quark model and diquark model.