Lee helped Korea claim the title for the third time in a row with a livewire performance in his team's 2-1 win over Japan in Hangzhou.
Nearly every able-bodied South Korean male is required to perform at least 18 months of military service, but the government rewards Asian Games gold medals and Olympic medals of any colour with an exemption.
Lee follows in the footsteps of Tottenham forward Son Heung-min, who won gold in Jakarta in 2018.
Coach Hwang said the exemption was "very different from playing football" and has high hopes for Lee's future.
"As long as the player has the Taeguk Warriors emblem on his shirt, he has the right and responsibility to play for Korea and play for its glory," he said.
"I am expecting his future success."
Lee, who joined PSG from Spanish side Mallorca in the summer, arrived late in Hangzhou and had been used sparingly on the way to the final.
He started against Japan but Korea found themselves a goal down after less than two minutes.
They leveled midway through the first half through Stuttgart forward Jeong Woo-yeong -- his tournament-leading eighth goal -- before Cho Young-wook struck the winner 10 minutes after the break.
Hwang said his team's win was "part of an ongoing process which is endless".
"We will soon be preparing for the Olympic qualifiers so this gold medal is only for today," he said.
"Our secret is that we have strengthened in defense and we take care of the uniqueness of each player."
This year's Asian Games, which were postponed by a year, featured under-24 squads plus overage players, similar to the Olympics.
Three qualifying places for the Paris Games are up for grabs at the under-23 Asian Cup in Qatar next April.
Hwang said qualifying for Paris is Korea's next goal but refused to let it weight too heavily on his mind.
"We don't always have to stay on our toes -- our mental state is very important," he said.
"Sometimes we have to relax as well. I'm not a very serious person, you can see a big smile on my face."
Japan got off to a sensational start to the game when Kotaro Uchino gave them the lead with less than two minutes on the clock.
But their team of players from the domestic J-League could not keep up with Korea's overseas-based line-up, and gradually faded as the match wore on.
Coach Go Oiwa said the game "left a lot to be desired".
"There was a tough battle for control of the ball -- sometimes we had it and sometimes we didn't but eventually we lost the game," he said.
"We want to improve."
Oiwa also set his sights on the Paris Games.
"It's not just the players who were here but everybody in the under-22 category," he said.
"We might make adjustments for the qualifiers but whatever changes we may make, the goal stays the same, which is to improve our level of play," he said.