I definitely thought the Stars could've won a second cup during the coaching tenures or Hitchcock and Tippett, and 2003 is the year I thought a chance for another cup slipped through their fingers the most.
In hindsight, 1998 is a year we really could've won it had Nieuwendyk not gotten injured the first game of the playoffs. He had his best regular season as a Star that year and we struggled to score after he went down (for example, we only scored 9 goals total in our 5 game series victory over Edmonton). It still would've been tough beating Detroit, and I take nothing away from them repeating that season. But our struggle to score combined with Nieuwendyk winning the Conn Smythe the next season has at times made me wonder about the 98 WCF vs Detroit. Our struggles scoring in the 98 playoffs also lead to us signing Brett Hull that offseason.
As for 2000, despite getting back to the finals and having a chance at repeating, I don't really view it as a missed opportunity. The Devils were simply better than us. The 2000 Stars team wasn't the same team that won the President's trophy the previous 2 seasons in addition to winning the cup the season before. While they were still among the best defensively (finishing 2nd, 1st and 3rd in GA the 3 respective years from 1998-2000), their offense really dipped this season, finishing 21st in GF after being 3rd and 8th the 2 previous years. We got outplayed by Colorado in the WCF that year and won because Belfour stole the series for us. Then in the finals we run into a New Jersey team who was our equal at shutting down opponents but could score more. People remember the Devils as a trapping team during that era when they won 3 cups, but the 2000 team could score, as the finished 2nd in GF that season (and lead the league in goals the next season). I've seen that most Devils fans consider the 2000 team to be the best of their 3 cup winning teams. Basically, the 2000 Stars team was fortunate to make it back to the finals and lost to a Devils team who was better, so I don't view it as a missed chance.
2003 was the year I thought we let a chance at a 2nd cup slip through our fingers. After Hitchcock and Belfour flamed out in 2002 (resulting in us missing the playoffs), we brought in Dave Tippett as our coach and retooled our roster. Marty Turco had an unbelievable first season as a starting goalie posting a then record 1.72 GAA. We were 6th in GF and 3rd in GA, and all this added up to us being the first seed in the West. Then Detroit and Colorado both lose in the first round and I believed the West was easily ours. Then Giguere comes along with his insane 2003 playoffs, and we lose the first 2 games at home in OT and never recover (including allowing a game tying goal with under a minute to go in the 3rd in game 2). Mentions Giguere's performance those playoffs instantly brings back the bad memories of this series for me. If we could've won this series, I definitely think we beat the Wild in the 2003 WCF.
I also believe we could've beaten the Devils had we had a rematch with them in 2003. This time we could've had home ice, plus our offense was much better this time around than in 2000 while our D was just as elite. Also, remember earlier when I said the 2000 team wasn't like the low scoring trapping team the Devils are remembered as during this era? The Devils team everyone remembers as a trapping team was the 2003 team, who was tied for first in GA but only 14th in GF. The Stars and Devils were once again defensive equals, but this time home ice and offense would've been in the Stars favor. And while I've heard the consensus among Devil fans is that the 2000 team was their best cup winning team, I've also heard similarly that 2003 was the weakest of the three, which I would agree with.
As for the Lightning, I don't really think they've blown a huge chance at a 2nd cup. 2011 was a last ditch run to get one more cup during the St. Louis/Lecavalier era, and it was apparent that it was a one year wonder. And our loss to the Blackhawks in the cup last season was a case of a young team having to learn how to win in their first deep playoff run, especially since they were playing the Blackhawks, the team that currently knows how to win best in those big games.