The 11-year veteran Lucic was not banned, but he was handed a $10,000 fine for hitting the 21-year-old Joseph when he didn't have the puck and then punching him as Lucic jumped on top of him.
Joseph, who covered up to protect himself from the attack, was not seriously hurt on the play which sparked a couple of other pushing and shoving matches as several of his teammates rushed to his aid.
Lucic was assessed two minor penalties for interference and roughing along with a 10-minute misconduct for the incident, which took place halfway through the third period of Edmonton's 5-2 loss to the Lightning.
Tampa Bay captain Steven Stamkos described Lucic's attack as a "cheap shot".
"You never want to see a guy take a cheap shot where it is premeditated like that," said Stamkos. "I wasn't a big fan of how he went after an unsuspecting player like that and hit him with a blindside hit."
The NHL's disciplinary department said in a news release that the fine was the maximum amount allowed under the players' collective bargaining agreement.