The team announced the move on Twitter on Friday.
Lee, 31, has four goals through 12 games this season for the Islanders. Johnston, 27, had dressed for one game this season, failing to record a point.
Islanders coach Barry Trotz had said on Wednesday that Josh Bailey was remaining in Florida while under COVID-19 protocol. Bailey was placed in protocol after receiving a positive test and missed Tuesday's game in Florida against the Panthers.
The Islanders host the Calgary Flames on Saturday in their first home game of the season as they open the new UBS Arena.