1995: Another posted mentioned Slava Fetisov who wasn't happy about his playing time under Jacques Lemaire, so he requested and was granted a trade to Detroit. Corey Millen was traded to bring in Neal Broten which sparked the offense down the stretch. Alexander Semak was traded to Tampa Bay which brought in Shawn Chambers and Danton Cole. Chambers in particular formed a good pairing with Scott Stevens for those playoffs.
2000: Brendan Morrison held out to begin the season and eventually requested a trade after he signed. Right after Morrison and Patrik Elias ended their holdouts, Lou traded Brian Rolston to Colorado to bring back Claude Lemieux. With Morrison/Elias back, the team had an overload of LW/C finesse types and Lou thought the team needed that pest element that Claude brought. With one more expansion draft looming, dealing Rolston also opened up a protection spot.
Denis Pederson started the season with an alternate captain's "A" but missed time due to injury. The Devils were juggling 15+ NHL caliber forwards that season when Scott Gomez unexpectedly forced his way onto the roster. Pederson seemingly felt like he was healthy enough to play but the team might have kept him on IR for some roster flexibility. Pederson was also unhappy with being shifted to RW from his preferred center spot.
Vadim Sharifijanov was a former 1st round pick who had decent AHL numbers and put up 27 points in 53 games in 1998-99. But he had difficulty getting ice time and Lou traded him to Vancouver for picks. Oddly Brian Burke called this his worst trade although he didn't elaborate. Sharifijanov would be back in Russia after one more year in North America. Possibly an expansion draft motivated move as this freed up another spot.
A couple weeks before the trade deadline, Vladimir Malakhov managed to make himself persona non grata in Montreal. He had missed most of the season with a knee injury but was spotted at a ski resort during the All-Star break. Montreal went on a winning streak after he came back, but during a home loss, the fans let Malakhov have it. Montreal would trade him to New Jersey for Sheldon Souray+. Dealing Souray for an impending UFA opened up another expansion protection spot.
Lyle Odelein was an impending free agent and had been feuding with head coach Robbie Ftorek for a couple seasons. With the emergence of rookie Brian Rafalski, Odelein's ice time dwindled and he requested a trade. He publicly said he had no problems with the players or Lou, it was all about how much he hated Ftorek. After acquiring Malakhov, Lou dealt Odelein to Phoenix for Deron Quint. Not sure if he would have been dressed in the playoffs, but Quint managed to get himself kicked off the team in short order. Scuttlebutt was that he showed up to practice hungover. Ironically, Lou would fire Ftorek after the deadline leading the media to wonder if dealing Odelein was unnecessary.
And then the Devils big deadline splash was finally trading Morrison+Pederson to Vancouver for Alexander Mogilny.
2003: No particular regulars missed out on the Cup. There was a rumor that Lou had a deadline deal to bring in Teemu Selanne, Marco Sturm, and Mike Ricci for Scott Gomez and Oleg Tverdovsky but that Selanne used his no trade clause to block it (he apparently didn't want to be traded period).
It wasn't a trade but Mike Danton managed to get himself suspended early in the season. He had earned the opening night 4th line center spot but refused to report to our AHL club after they wanted to send him down. Not sure if he would have gotten into the playoff lineup, but with Joe Nieuwendyk injured the team turned to Jiri Bicek and Mike Rupp in the SCF.