Like charging a laptop while charging with a low capacity charger both keep the battery charged and the display on and CPU running. You do not see any flickering in performance. The BMS in the Li-ion battery pack uses the excess power of the charger to charge and if to low the BMS starts discharging the battery just a little bit to compensate. The specs on solar and BMS says that it is not possible to charge and discharge at the same time. That said it would mean a lamp connected to the controller load leads would basically stop the charging process to the BMS and the battery. At night, Okay but at daytime when the sun is shining on the solar panels, what then? Same as with the laptop, the excess is used to charge the battery through the BMS, all power from the solar panel is going strait to the load. It is a process of filling up a bucket and it does not matter from which it is filled. The BMS takes always care of dangerous discharge levels, it's what it does best. The solar controller distributes the power accordingly, it's what it does best. The load (Lights) leads should be rated to draw current at what the solar controller is rated at for solar current input, basically pass through.
