An assembly and method for completion of lateral wellbores is disclosed. The completion assembly includes a junction fitting with main and lateral legs, and a lateral completion string and anchoring device connected to the downhole end of the lateral leg and the uphole end of the junction fitting, respectively. A working string, positioned within the lateral leg, anchoring device, and lateral completion string, includes a setting tool that is removably connected to the anchoring device and a completion tool assembly located within the lateral completion string. The completion assembly is run by the working string into the wellbore. After setting the anchoring device, the working string conveys the completion tool assembly within the lateral completion string for gravel packing, fracturing, frac-packing, acidizing, cementing, perforating, and inflating packers, for example. After wellbore completion, the completion tool assembly is removed through the lateral leg of the junction fitting.