Martel was brought in via trade by the Panthers from the Lightning on Thursday in exchange for Anthony Greco.
Martel signed a one-year, two-way contract with the Lightning on Thursday, Joe Smith of The Athletic reports.
Martel has received a qualifying offer from the Lightning, Renaud Lavoie of TVA Sports reports.
Martel played Tuesday for the first time since Jan. 10 and recorded an assist in a 6-3 win over Calgary.
Martel is once again a healthy scratch after playing two games last week.
Martel dressed for three straight games right before Christmas after being a healthy scratch for the previous five weeks.
Martel is back with the Lightning on Sunday after a conditioning assignment with AHL Syracuse.
Martel survived the final cut and is now a member of the Lightning, reports Nick Kelly of the Tampa Times.
Martel was claimed off waivers by the Lightning on Saturday, Elliotte Freedman of Sportsnet.ca reports.
Martel was waived by the Flyers on Friday, Renaud Lavoie of TVA Sports reports.