You should be able to setup multiple LoRa Server instances as a cluster. Also, you should be able to setup a Redis cluster (using the tools provided by Redis). So from this side, LoRa Server is pretty scalable.
Please note that when you broadcast thousands of (downlink) messages that the number of gateways might become a concern too. Also, will you be using Class-A or Class-C for this? In case of Class-A LoRa App Server will keep a queue per device. When a receive-window occurs, it will pop the first item from this queue and sends it to the node.