The Castleconnell 24-year-old middleweight is to meet with the doctor who cares for Manchester's welterweight champion Ricky Hatton.
"I will talk to him and see what he thinks about when I will be able to box again," Andy Lee told Leader Sport.
"He is going to re-stitch the wound," added Lee.
The same eye injury had kept the former St. Francis Boxing Club Olympian out of the ring for the last eight months, before the weekend's return on the undercard of Bernard Dunne's world title fight at the O2 in Dublin.
"It was a clash of heads in the first one or two coming-togethers in round one," recalled Andy Lee of the cut over his right eye.
"I'm a southpaw so my right side is always going to be open to opponents, so there is always a danger when the boxers come-together," explained the Limerick man who fights out of Emanuel Steward's Kronk Gym in Detroit.
When Lee stepped into the ring in front of a capacity 9,000 crowd in The O2 last Saturday it was exactly one year since his only professional loss to Brian Vera.
Lee had hoped that last Saturday would see him get back on the road to world title contention following the lengthy lay off to recover from January's surgery to repair a cut eye suffered in his win over Willie Gibbs in Limerick last July.
"A win is a win," said Lee of last Saturday's victory against the former European title challenger Alexander Sipos from Germany.
Sipos came to the venue with 19 wins on his record and a reputation as a tough, durable and seasoned fighter.
"I know that people are saying that I wasn't great, but I was happy," Andy Lee explained.
"I went ten rounds and that was great after being out of the ring for so long.
"It wasn't spectacular or impressive, but it was a good mental win."
Referee Emile Tiedt scored the contest 99-91 in favour of the Castleconnell middleweight and although Lee always looked comfortable Alex Sipos did present the Limerick man with a tricky obstacle to surmount.
"I felt that I won seven of the rounds and that he won three," was Andy Lee's honest assessment of his 18th pro-fight.
"Yes it was an ugly fight, but that was because of the clash of styles - he was rushing in and not allowing me to get in some solid boxing."
In the immediate aftermath of his latest win Lee was relieved to earn the referee's decision.
"That was as tough as I expected. Alex is tough and has a lot of pride. He's a hard fighter and he forced me back. The ten rounds will stand to me and I will move on from here. I was very rusty because of the long lay off, but there are no excuses.
"Thankfully I won the fight so it's onwards and upwards from here," said Lee.
"I knew he had a good strong style - I went 10 rounds and that was good for me and I was happy with myself. It is another win in my development and now I need to move on again."
Lee looked rusty in the opening round and although he caught Sipos with a good left hand the German recovered to connect with a barrage late in the round which left the Limerick man nursing a cut over his right eye.
Lee steadied himself in the second round however and proceeded to take control of the fight keeping the physically powerful Sipos at bay with a stinging right jab.
The third and fourth rounds followed a predictable pattern with Lee in complete control. Sipos looked a one-dimensional fighter, but he did catch Lee with a dangerous left in the fifth round.
Andy Lee regained control in the sixth and dropped Sipos with a stunning right hook late in the round - Sipos survived referee Emile Tiedt's standing eight count.
Sipos struggled through round seven and eight, but rallied significantly in the last two rounds of this ten-round contest. The German charged forward in search of a knockout and although he caught Lee with several dangerous right hands the Limerick man never looked in any real danger.