The Lightning's championship came in 2004. The Stars won theirs in 1999.
They will play the first Stanley Cup Final contested entirely at one neutral site in front of no fans.
Game 1 of the best-of-7 series is at Rogers Place in Edmonton on Saturday (7:30 p.m. ET; NBC, CBC, SN, TVAS).
"It might be one of the hardest Cups to ever win," Lightning coach Jon Cooper said. "Whoever raises this Cup, they'll have earned this one, I'll tell you that."
Tampa Bay reached the Cup Final by defeating the Columbus Blue Jackets and Boston Bruins each in five games, and the New York Islanders in six games in the Eastern Conference Final.
The Stars defeated the Calgary Flames in six games, the Colorado Avalanche in seven games, and the Vegas Golden Knights in five games in the Western Conference Final.
Here are seven Stanley Cup Final storylines to follow:
Lightning trying to make history
Tampa Bay can become the first team in the NHL expansion era (since 1967-68) to win the Stanley Cup the season after being swept in the first round of the Stanley Cup Playoffs.
Tampa Bay lost four games to Columbus in the Eastern Conference First Round last season, becoming the first Presidents' Trophy winner to be swept in the first round.
"We put that behind us," Lightning defenseman Victor Hedman said.
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During the NHL Original Six era (1942-67), two teams won the Cup after being swept in the first round the previous season; the Chicago Black Hawks defeated the Detroit Red Wings in six games in the 1961 Cup Final after being swept in the NHL Semifinals (first round) by the Montreal Canadiens in 1960. The Toronto Maple Leafs defeated the Canadiens in six games in the 1967 Cup Final after Montreal defeated Toronto in four in the semifinals in 1966.
"You look at what happened last year, we took it on the chin, and rightfully so, we deserved to take it on the chin," Cooper said. "But to counterpunch the way we have this year, good on the guys."
Bowness' big chance
Stars coach Rick Bowness, in his 45th year in professional hockey, the last 38 as a coach or assistant, is four wins from winning the Stanley Cup for the first time. To do it, he has to defeat one of his many former teams.
Bowness was an associate coach with the Lightning under Cooper from 2013-18. Cooper, who hadn't coached in the NHL prior to 2013, credits Bowness for teaching him a lot about the League, including where the entrance was to all the arenas.
They helped the Lightning reach the Cup Final in 2015, when Tampa Bay lost to Chicago in six games. Bowness also went to the Cup Final as an assistant with the Vancouver Canucks in 2011, when they lost to the Boston Bruins in seven games.
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This will be the first time a coach and his former assistant have faced each other as coaches in the Stanley Cup Final, according to the NHL Coaches' Association,
"There's no better satisfaction than what he's living right now," Stars general manager Jim Nill said of Bowness. "It's because of hard work, how he treats people and who he is."
Vasilevskiy against Khudobin
Barring injury, it appears a Russia-born goalie will win the Stanley Cup as a starter for the second time in NHL history, joining Nikolai Khabibulin, who won it with the Lightning in 2004.
Tampa Bay goalie Andrei Vasilevskiy is 14-5-0 with a 1.82 goals-against average and .931 save percentage this postseason.
Dallas goalie Anton Khudobin, who in the regular season was the backup to Ben Bishop, Vasilevskiy's former teammate with Tampa Bay, is 12-6-0 this postseason with a 2.62 GAA, .920 save percentage and one shutout.
Vasilevskiy is the only goalie who played in the conference finals who started every game for his team in the postseason (19). He has allowed two or fewer goals in eight of the past nine games.
Khudobin wasn't supposed to be the starter for the Stars, but Bishop has been unfit to play. Khudobin has won eight straight games when making at least 30 saves.
Jamie Benn is in the discussion for the Conn Smythe Trophy as postseason MVP.
Benn leads Dallas forwards with 18 points (eight goals, 10 assists) in 21 games. The Dallas captain scored five points (three goals, two assists) in five games against Vegas, including a goal in each of the last three games.
Video: Breaking down Jamie Benn's big performance in the WCF
Benn scored 39 points (19 goals, 20 assists) in 69 games this season, the lowest single-season point total of his NHL career, excluding the shortened 2012-13 season, when he scored 33 points (12 goals, 21 assists) in 41 games.
"He's our leader and our captain, and whenever there are big moments he's always the front-runner in changing the momentum or keeping the momentum," Stars center Tyler Seguin said. "He's playing the best that I've seen him, and I think he's still got another level."
Hedman against Heiskanen
Hedman was voted the Norris Trophy winner as the best defenseman in the NHL two seasons ago, was third in voting last season, and is one of three finalists this season. The 29-year-old is arguably Tampa Bay's favorite to win the Conn Smythe Trophy through three rounds.
Stars defenseman Miro Heiskanen likely will also become a perennial Norris Trophy contender, and the 21-year-old is a contender for the Conn Smythe Trophy.
Hedman is averaging 26:31 of ice time per game in the postseason; Heiskanen is averaging 25:43.
Heiskanen leads defensemen with 22 points (five goals, 17 assists) in 21 games and is one of 11 defensemen in NHL history to score that many points in a single postseason.
Hedman leads defensemen with nine goals, the first time a player at the position has scored that many in a single postseason since Brian Leetch scored 11 for the New York Rangers in 1994, when he won the Conn Smythe Trophy and Stanley Cup.
Maroon can join small club
Lightning forward Pat Maroon has a chance to become the third player in the NHL expansion era to win the Stanley Cup in back-to-back seasons with different teams.
Maroon won the Stanley Cup last season with the St. Louis Blues. He signed a one-year, $900,000 contract with the Lightning on Aug. 24, 2019.
"We've got to go for four more [wins]," Maroon said.
The last player to be a part of back-to-back Cup championships with different teams was Mark Hartigan, with the Anaheim Ducks in 2007 and Red Wings in 2008.
Hartigan's name is not on the Stanley Cup, however, because he didn't meet the games-played criteria either time (at least 41 games played in the regular season or one game played in the Stanley Cup Final).
Before that, Cory Stillman won the Stanley Cup with the Lightning in 2004 and the Carolina Hurricanes in 2006. The Stanley Cup was not awarded in 2005 because of a work stoppage.
Claude Lemieux is the last player to play in the Cup Final with different teams in back-to-back years and win it each time. He did it with the New Jersey Devils in 1995, when he won the Conn Smythe Trophy, and in 1996 with the Avalanche.
Will Stamkos play?
Steven Stamkos hasn't played in the postseason because of a lower-body injury he sustained before the Lightning reconvened in Tampa Bay for training camp in July. The forward has not played since Feb. 25.
But Stamkos has not been ruled out for the Cup Final, though he won't play in Game 1; he was on the ice for the postgame celebration when the Lightning accepted the Prince of Wales Trophy as the Eastern Conference champions Thursday.
"Even though [Stamkos] is not playing he's still the leader of this team," Hedman said of the Lightning captain. "He's such a good influence in the room, in practices, morning skates. He's such a big reason why we're here where we are."