We study the problem of repairing erasures in locally repairable codes beyond the code locality under the rack- aware model. We devise two repair schemes to reduce the repair bandwidth for Tamo-Barg codes under the rack-aware model, by setting each repair set as a rack. The first repair scheme provides optimal repair bandwidth for one rack erasure. We then establish a cut-set bound for locally repairable codes under the rack-aware model. Using this bound we show that our second repair scheme is optimal. Furthermore, we consider the partial-repair problem for locally repairable codes under the rack-aware model, and introduce both repair schemes and bounds for this scenario.