A look ahead at the offseason for the Lightning and Kings plus more speculation about what the summer might hold for the Jets and Islanders in the Sunday NHL Rumor Roundup.

WHAT NEXT FOR THE LIGHTNING AND KINGS?

ESPN.COM: Kristen Shilton looked at what could be a difficult offseason for the Tampa Bay Lightning following their first-round elimination by the Toronto Maple Leafs.

Figuring out how to free up more salary-cap space should be a priority. Veterans like Alex Killorn, Corey Perry and Ian Cole are eligible for unrestricted free-agent status this summer. They also have limited trade capital with just three picks in this year’s draft.

Tampa Bay Lightning forward Alex Killorn (NHL Images).

SPECTOR’S NOTE: Lightning general manager Julien BriseBois did a fine job managing his limited cap space to maintain a contender for the past three years. However, he now faces a different challenge in figuring out how to restore the depth around his core talent before their best seasons are behind them.

BriseBois could find it easier should the salary cap increase this summer by more than the projected $1 million. Otherwise, he could face another offseason shedding more roster depth and trying to find suitable replacements at cheaper prices.

Ryan S. Clark examined what could be in store this summer for the Los Angeles Kings following their second straight first-round elimination by the Edmonton Oilers.

The Kings will have to ensure they’ve got sufficient cap space to re-sign restricted free-agent forward Gabriel Vilardi. They’ll also have to decide what to do with pending unrestricted free agents Joona Korpisalo and Vladislav Gavrikov.

They’ll also have to decide what to do with goaltender Cal Petersen, who’s completing the first season of a three-year contract worth $5 million annually. The struggles of Petersen and now-former Kings goalie Jonathan Quick led the Kings to turn to Pheonix Copley for large stretches of the season before acquiring Korpisalo at the trade deadline.

SPECTOR’S NOTE: It’ll be interesting to see how general manager Rob Blake addresses this situation. Vilardi’s performance this season has him in line for a significant raise while Korpisalo and Gavrikov were solid additions who are worth retaining if there’s sufficient cap room to do so.

Trading Petersen could free up valuable cap space to re-sign Vilardi and retain Korpisalo and/or Gavrikov. Given his struggles over the past two seasons, however, it’s unlikely they’ll find any takers unless they retain a portion of his salary or take back a bad contract in return.

LATEST ON THE JETS

WINNIPEG SUN: Ted Wyman reports Jets winger Kyle Connor isn’t interested in being part of a roster rebuild at this stage in his career. “I don’t think anybody in that locker room wants to be part of a rebuild,” he said. Connor is among the few Jets stars with more than one year remaining on his contract.

Mark Scheifele, Blake Wheeler, Connor Hellebuyck and restricted free agent Pierre-Luc Dubois are all a year away from unrestricted free-agent eligibility. If any or all of them are moved this summer, Wyman believes that will at least constitute a retooling, if not a rebuild.

SPECTOR’S NOTE: Much of the focus on a possible Jets rebuild is based on shipping out Scheifele, Wheeler, Hellebuyck and Dubois and using the returns to build around players like Connor, Josh Morrissey and Nikolaj Ehlers who still have term on the contracts beyond next season. It hasn’t taken into account that those players might not want to be part of that process

Connor pointed out he has no say in what management does. Nevertheless, his comments could have some impact on their offseason decisions. Instead of trading those players for draft picks and prospects, perhaps they seek returns that provide a quicker turnaround in the Jets’ fortunes.

Speaking of Dubois, Wyman reported he was dismissive of the rumors about his future. Nevertheless, the 24-year-old center made no secret that he’d like to choose where he plays once he becomes a UFA.

“The right to choose is something that personally, it gives you power,” said Dubois. “You can make your decision and not just go where you’re told. So for me, that’s something that’s pretty important.”

Speculation has linked Dubois to the Montreal Canadiens since his agent last summer hinted that he might like to play for them one day.

SPECTOR’S NOTE: Dubois playing coy over whether he’s interested in a long-term deal with the Jets. His comments will only stoke speculation that he could be traded to the Canadiens this summer.

Hellebuyck has no idea if he’ll be part of the Jets future beyond this season. “I don’t know what their plans are, and I don’t know if I’m in it, to be honest,” he said. “If they decide to move me, that’s their call. If they decide to try to talk, I haven’t really thought about that yet.”

SPECTOR’S NOTE: Hellebuyck also isn’t interested in a rebuild. “My main goal is to win a Stanley Cup and I’m running out of time,” said the 30-year-old goaltender.

Scott Billeck reported Scheifele was non-committal about his future. He learned his lesson from last year when season-ending remarks about doing what’s best for him and his career sparked weeks of trade speculation.

“I think it’s too early to talk about,” said Scheifele. He plans to take time in the coming days and weeks to think about it and figure things out.

SPECTOR’S NOTE: I’ll be very surprised if the Jets return next season with their current core intact. They’ve been in decline over the past five seasons. General manager Kevin Cheveldayoff has been patient to a fault but it’s apparent that this group isn’t getting any better. Changes are necessary and could be coming as early as June in the lead-up to the 2023 Draft in Nashville.

NHL WATCHER: cited Sportsnet’s Jeff Marek on the “32 Thoughts” podcast wondering if Blake Wheeler might be a fit with the Philadelphia Flyers or Boston Bruins given the questions about the futures of Flyers center Sean Couturier and Bruins captain Patrice Bergeron. Marek believes Wheeler fits the mold of those teams.

SPECTOR’S NOTE: If Chuck Fletcher were still the Flyers GM, then yes, Wheeler would fit their mold. Not anymore. The Flyers are rebuilding and Wheeler (who turns 37 in August) is too old to be a suitable part of that process. As for the Bruins, I think they’d be more interested in someone who’s younger as a possible replacement for Bergeron.

BIG DECISIONS FACING THE ISLANDERS

NEW YORK POST: Ethan Sears believes the New York Islanders face many organizational questions heading into this offseason.

The first is whether general manager Lou Lamoriello will be back. It’s unknown if the 80-year-old has signed a contract extension to stay on as president and general manager of the Islanders for next season. His current deal is believed to expire at the end of this season.

Lamoriello or his replacement will have to decide if they’ll tinker with the current roster or make significant changes. Semyon Varlamov, Pierre Engvall, Scott Mayfield and Zach Parise are their notable UFAs. Veterans still under contract like Josh Bailey, Cal Clutterbuck and Matt Martin could be trade or contract buyout candidates.

With centers Bo Horvat and Mathew Barzal under long-term contracts, Sears wondered if Jean-Gabriel Pageau or Brock Nelson might be traded for resources that could be deployed elsewhere in the lineup.

SPECTOR’S NOTE: Sears doesn’t expect the Islanders to engage in a roster teardown and neither do I. However, they must bolster their offense if they hope to be more than a marginal playoff contender in the Metropolitan Division. That could involve one or two cost-cutting moves to free up sufficient cap space to address that issue this summer.