Lee was designated for assignment by the Padres on Monday.
The Padres needed to clear a roster spot for Dillon Overton -- who was recently claimed off waivers from the Mariners -- and Lee was the roster casualty. The 25-year-old, who compiled a 5.62 ERA and 2.00 WHIP across eight innings with the big club earlier in the year, will likely report to Triple-A if he passes through waivers untouched.