The star full-back has been ruled out of the Ospreys' EDF Energy Cup semi-final with Gloucester this weekend and remains a major doubt for the Heineken Cup quarter-final against Munster on April 12.
Now Byrne, 28, faces a fight for fitness to be named in the Lions touring party with coach Ian McGeechan confirming yesterday that he will name his squad for South Africa just nine days later.
Ospreys coach Sean Holley said: "Lee has had a scan which confirmed inflammation of the tendon.
"We do not know the full extent of the injury yet and we're seeking further medical opinion but it's a hammer blow to lose the best full-back in the world this weekend
"We hope to hope he will make the Munster game but the prognosis isn't brilliant. We don't think it will affect his Lions hopes but we just don't know - we'll just have to wait and see."
Byrne faces stiff competition from Ireland Grand Slam winner Rob Kearney and England's Delon Armitage for the number 15 jersey.
His Ospreys team-mate Tommy Bowe returned to the Welsh region yesterday following his try-scoring exploits at the Millennium Stadium.
But the Ireland wing insists the historic Slam success is only the beginning as he chases a treble with the Ospreys and a Lions place.
Bowe said: "It's been a huge weekend for Irish rugby and a hectic few days but it's great to be back with the lads. "They made me sit on my own for breakfast and I've got to make new friends again," he said.
"Of course, I can reach that peak again as a rugby player. We're still in three competitions and we're aiming to win all three. This season has the potential to only get better."