The CFL club made the announcement Tuesday, two days after Lulay was injured while running for a touchdown in a 36-14 home win over the Montreal Alouettes.
"We're disappointed but we know he'll be back," Lions head coach Mike Benevides said.
The Lions said that Lulay, the CFL's 2011 outstanding player, will be re-evaluated following B.C.'s game in Winnipeg on Sept. 27.
"I'm not helping the team if I can't play so I want to bet back as soon as possible," Lulay said. "I don't regret trying to score on the play, it's just an unfortunate result."
The six-foot-two, 217-pound Lulay completed a 14-yard TD run by lowering his right shoulder near the goal-line and going through Montreal defensive back Geoff Tisdale. Lulay hurt the same shoulder late last season while throwing a pass against the Hamilton Tiger-Cats and missed the final five games of the regular season.
And in 2007, he required surgery on his right shoulder to repair a torn labrum he suffered while playing for the Berlin Thunder of now-defunct NFL Europe.
Benevides wouldn't say whether sophomore Thomas DeMarco or veteran Buck Pierce will start when B.C. (7-4) visits the Saskatchewan Roughriders (8-3) on Sunday. Benevides is expected to name his starter Wednesday, however.
"We're both going to prepare to play this week," DeMarco said of he and Pierce. "We're just going to see where the reps go."
The five-foot-11 200-pound DeMarco came on to replace the injured Lulay against Montreal and finished 4-of-6 passing for 47 yards and a 14-yard TD strike to Marco Iannuzzi for his first CFL career touchdown pass.
The 24-year-old Californian, who played his college football at Old Dominion, also ran three times for 13 yards. DeMarco has completed 15-of-24 passes for 148 yards with a touchdown and no interceptions in his brief CFL tenure.
Pierce, 31, is in his second stint with B.C. He began his Canadian professional career with the Lions in '05 and spent five seasons with the club — earning a Grey Cup ring in 2006 — before being released March 9, 2010.
Pierce signed with Winnipeg about a month later. Pierce battled injuries throughout his time in Manitoba but his best season with the Blue Bombers was 2011 when he appeared in 16 regular-season games and led the squad to the Grey Cup.
But the 2011 campaign ended miserably for Pierce and the Bombers, who lost a 34-23 decision to the Lions at B.C. Place. Lulay was named the Grey Cup MVP after completing 21-of-37 passes for 320 yards and two second-half TDs.
The six-foot-two, 195-pound Pierce finished 19-of-37 passing for 250 yards for Winnipeg in the Grey Cup game with two touchdowns and an interception. He also added 17 yards on four carries.
Pierce, who played collegiately at New Mexico State, is in his ninth CFL season. He has appeared in 114 career games, passing for 15,059 yards and 73 touchdowns with 62 interceptions. He has also rushed for 1,666 yards on 229 carries (7.3-yard average) and scored 13 TDs.
The Lions re-acquired Pierce from Winnipeg on Sept. 8 for receiver Akeem Foster.
Lulay, 29, in his fifth CFL season, is the league's second-leading passer with 2,787 yards. The former Montana State star has thrown 19 TDs with 11 interceptions and added 286 yards rushing, averaging 7.2 yards per attempt, with two touchdowns.