Do I need to add the ground wire from the transformer ground lug to a common ground connection of my station?

The ground lug at the transformer bottom is meant for use with a dedicated ground rod when the transformer is installed up to 10 feet (3 meters) above ground. If it is not practical for you to add dedicated ground rod for an EFHW antenna, just omit that connection and ground the coax shield of the feed line to a  station ground, entry connector plate or dedicated ground rod with lightning arrestor at the entrance to the home/radio room.