Newsday’s Arthur Staple was first to report the transaction.
Gudlevskis, a native of Aizkraukle, Latvia, went 15-10-11 with the AHL’s Syracuse Crunch this past season. He had a 2.65 goals-against average a .897 save percentage.
The Lightning will ride with a tandem of Andrei Vasilevskiy and Peter Budaj in net. The team parted ways with Ben Bishop in February.
Verhaeghe, a third-round pick of the Maple Leafs in 2013, was acquired by the Islanders from Toronto in a trade involving Michael Grabner in 2015. The 21-year-old split the 2016-17 campaign between the AHL’s Bridgeport Sound Tigers and ECHL’s Missouri Mavericks.