"His loss will be felt profoundly by his teammates, coaches, supporters and all who had the privilege of knowing him," the Lions said in a statement on Friday.
"Our deepest and most heartfelt condolences go to Hyron’s wife, Maiglin, their young sons, and the entire Andrews family.
"We hold them in our thoughts during this time of unimaginable grief and ask that their privacy be respected as they mourn."
French media reports said Andrews, 31, was found unconscious in a shower cubicle at a hotel on the Ile de Re in France, where the team had been staying since Tuesday.
Emergency services were called shortly after 10 a.m. and attended to the player, who was in cardiorespiratory arrest. Attempts to resuscitate him were unsuccessful, the reports added.
The Lions have offered no details around the circumstances of Andrews' passing, but confirmed Saturday's game will go ahead.
"In honour of Hyron, the Lions will fulfill their opening match of the Champions Cup against La Rochelle," the team statement continued.
Andrews had a spell with the Sale Sharks in England and played for the South African under-20 side, but was not a capped senior international.
His death comes 10 years to the day after Munster coach Anthony Foley passed away at the age of 42 in his Paris hotel ahead of a Heineken Cup match against compatriot Ronan O’Gara’s Racing 92.
O’Gara is now the coach of La Rochelle and according to Irish media visited the Lions at their hotel to offer his condolences.