Upon arriving in intensive care they were sedated by hospital staff.
Lee said the situation could have resulted in one or both players dying had they not been in the company of others.
"If there hadn't been two other people at the unit we could have been talking about a tragedy here tonight," Lee said on NRL360 on Fox Sports last night.
"It was very serious. One of the players has liquid on his lungs so that would indicate it was potentially a life-threatening health issue.
"It could have been tragic and we're just thankful it's been averted."
With both players suffering the same adverse reaction, it is believed the pair had shared their respective painkillers.
Lee said the players had not been using illicit drugs and they had not been drinking energy drinks, and there was no evidence the pair were consuming alcohol. He had visited the pair yesterday afternoon but they were in no condition to discuss the matter.
"I've seen both the players upstairs and they're pretty knocked around," Lee told the
Sydney Morning Herald.
"At this stage they're not in a state where they can communicate. Their vital signs are on the up. "This has brought a great deal of relief and we hope they will make a full recovery. They were prescribed a level of medication - not taken for fun - taken for pain. It is becoming clear that they took too much of that medication."
Lee explained the players were prescribed the painkillers by medical specialists after Walker underwent surgery on his broken left-hand and Gray had an operation on his right knee, following the Rabbitohs sudden-death NRL semi-final defeat to Cronulla last Sunday.
"It will become clear that they had actually taken more than the regulated amount of prescribed medication," Lee said.
"I think they are fortunate that at the time the alert was raised to get the ambulances to their homes and to get them treated."
South Sydney contacted the NRL integrity unit early yesterday and an investigation was quickly launched.
NRL chief executive Dave Smith expressed his concern for the pair and said the integrity unit's investigation would be thorough.
"What we know is two young men have ended up in hospital in a pretty seriously ill condition," Smith said.
"I think one was quite serious overnight but I think they're both stable now. Our priority is to make sure ... they get the best care ... and if we need to investigate further then we'll do that."