Mr Galbraith, a respected former neurosurgeon, served at Westminster as an MP and was elected to Holyrood shortly after the Scottish Parliament was formed.
He had undergone a lung transplant in 1990, and was one of the longest surviving people to have had the procedure.
Ms Lamont said: "Sam was a wonderful man. A great doctor, an inspiring colleague and dedicated family man.
"Sam was a great champion of the NHS, and he himself was a great example of how it can transform lives.
"We will all miss his vigour, his support and his candour. Our thoughts are with his wife and family."
Margaret Curran MP tweeted: "Such sad news about Sam Galbraith. We'll all miss his passion, wit and deep commitment to Labour vales. A huge loss to the Labour family."
Deputy First Minister Nicola Sturgeon tweeted "Very sad to hear this. My thoughts are with his wife, family & friends."
Earlier, Alistair Darling, leader of the Better Together campaign and a family friend issued the statement confirming his death.
The former Labour Chancellor said: "Sam was a brilliant neurosurgeon, a dedicated politician, and a very dear friend.
"But above all, he was devoted to his family, to Nicola and their three daughters - Mhairi, Heather and Fiona - who are foremost in our thoughts.
"They have asked for their privacy to be respected at this time.
"Sam was believed to be the world's longest-surviving lung transplant patient. It was extraordinary how he continued to contribute and achieve so much throughout the 25 years that he lived with his condition.
"Sam's professional life and immense talents were devoted to the care and betterment of others, through the National Health Service and in his deep political commitment. He was a great humanitarian. His work and his life touched countless lives."
Mr Galbratih also held the environment sport and culture ministerial post in the Scottish Executive, before quitting on health grounds in 2001. Prior to that, he was a Scottish Office minister in Tony Blair's first administration for two years until 1999.
Before entering politics, Mr Galbraith's skills were widely respected as a neurosurgeon based at the Southern General Hospital in Glasgow.