Jason Zucker scored twice, and Tage Thompson, Alex Tuch and Rasmus Dahlin each scored for the Sabres (29-17-5), who have won three straight games and have 18 wins in their past 22 games (18-3-1).
Lyon, who made 13 saves in the first period, won his ninth straight game, tying a Sabres record (Gerry Desjardins, 1976-77).
David Rittich made 16 saves for the Islanders (27-19-5), who returned home from a 3-3-1 road trip, and shut out for the first time this season.
Zucker gave the Sabres a 1-0 lead 33 seconds into the second. Rittich made a right pad save on a Jack Quinn wrist shot from the slot before Zucker beat Rittich glove-side.
Thompson extended the lead to 2-0 at 19:47 of the second. Off the rush, Zach Benson skated behind the net and found Thompson, who had an empty net with Rittich sliding to the glove-side post.
Zucker scored his second of the game 25 seconds into the third period for a 3-0 lead. Maxim Shabanov turned the puck over before Ryan McLeod found Zucker cutting into the low slot.
Dahlin made it 4-0 with an empty-net goal at 14:02 of the third, with Rittich off for an extra skater.
Tuch scored at 14:38 of the third for the 5-0 final, deflecting a Mattias Samuelsson wrist shot from the slot.
Islanders forward Bo Horvat returned to the lineup after missing nine games with a lower-body injury.
New York defenseman Ryan Pulock is day to day and did not play because of an upper-body injury.
