"I don't have any words right now - one try and one win, I might retire!" a jubilant Lynagh told ITV.
Born in Italy but a former England junior international, the 23-year-old is the son of ex-Australia great Michael Lynagh, a World Cup winner in 1991, and said he would take on board his father's advice to him.
"Celebrate, refocus and go again. (There is) no point over celebrating one win - you have got to back it up," he said.
"Looking at them right now – dad is almost in tears, my grandad in Treviso will be over the moon, they will be so happy and I can't wait to celebrate with them. This is one of the best moments of my life."
Wallabies great Michael Lynagh was left emotional at watching son Louis's terrific debut. (Dan Peled/AAP PHOTOS)
Lynagh was strong on defence all game and took his chance to score in the second half when five-eighth Paolo Garbisi put in a superb grubber and the wing won the race to the ball and the tryline.
"It's an amazing thing that we have been working towards all week, there was something in the air and I felt like we could win," Lynagh said.
"We had a few players coming back from injury and it clicked for us. I couldn't ask for a better game to be part of."
Italy's Argentine head coach Gonzalo Quesada said the victory was built on strong defence and believes this can be a stepping stone to greater things with a final Six Nations clash against Wales in Cardiff next weekend.
"It's a good day for this team and it was a tough game," Quesada told the BBC. "I think we managed to become good in the second half. It's a special day though, it's a step in the growth of the team. I'm happy for them to experience a win.
"It's something we can find in every game. We have been consistent in defence - even in Ireland (a 36-0 loss) we kept on defending and putting our bodies on the line. It's an amazing feeling for a coach.
"We have created a special group who have worked tirelessly."
