Ladd opened the scoring 51 seconds into the game when he beat Vasilevskiy with a shot to the far side.
"First two periods, I thought we did a good job and we were able to get the pucks deep," Ladd said. "They are a talented offensive team, so we wanted to play as much as we could on our end of the ice."
Lee scored his 10th goal of the season at 10:25 of the first period to give the Islanders a 2-0 lead. Tavares set it up with a behind-the-back feed.
Nelson made it 3-0 lead at 7:09 of the second period with a shot that beat Vasilevskiy on the glove side.
"This is a good win against a tough team to beat in any building, especially at home," Bailey said. "We'll definitely this take one. Obviously they pushed late, but we got it done."
Lee's second goal was scored on the power play at 1:05 of the third period. Bailey set Lee up in front of the net, where he scored on the rebound of his own shot to make it 4-0.
"[The Lightning] are in the position that they are in, so we knew we had to come in here and work and play a good 60 minutes," Lee said. "Although we had a couple of letdowns, I thought we really put together a good game."