Alnefelt inked a three-year contract with former club HV71 (Sweden) on Tuesday.
Alnefelt was assigned to AHL Syracuse on Saturday.
Alnefelt has been named the AHL Player of the Week for the period ending Jan. 29.
Alnefelt was reallocated to AHL Syracuse on Saturday.
Alnefelt made his NHL debut Thursday in relief. He made seven saves on 10 shots in a 9-3 loss to the Panthers.
Alnefelt was added to the active roster for Tuesday's game against Montreal, Erik Erlendsson of LightningInsider.com reports.
Alnefelt was promoted from AHL Syracuse to the taxi squad Monday.
Alnefelt is one of three goaltenders who may be in line for Tuesday's game against Montreal.
Alnefelt will get the start in Friday's preseason tilt with Carolina.
Alnefelt signed a three-year, entry-level contract with the Lightning on Saturday.