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 a 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 pass-thru SO239 or with lightning arrestor at the entrance to the home/radio room. The grounding of all coaxial cable shields at the entrance to the home is required by National Electrical Code NEC 810