Lookman became the first player to score a hat-trick in a European final since 1975 to secure Atalanta's first ever continental trophy.
The side from Bergamo have long lived in the shadow of nearby giants AC and Inter Milan.
However, they have enjoyed a golden era under Gian Piero Gasperini, reaching the Champions League on four occasions, and now have silverware to show for it.
"To win it with Atalanta is perhaps one of the football fairytales that rarely gives scope for meritocracy," said Gasperini.
"It doesn't always come down to cold hard numbers or super leagues but shows teams without huge budgets can achieve big things."
Leverkusen have made a habit of late fightbacks in their remarkable run to winning a first ever Bundesliga title without tasting defeat.
But this time they failed to dig themselves out of a hole created by a slow start.
"It's a shame that the time it didn’t work out for us was in a final," said Leverkusen midfielder Granit Xhaka.
"It's bitter, definitely, we lost a final today but we go on and we'll make up for it on Saturday (in the German Cup final).
Atalanta's more purposeful play in the opening stages was rewarded after just 12 minutes.
Davide Zappacosta got to the by-line and Lookman caught Exequiel Palacios napping to fire into the top corner at the back post.
The Nigerian has at times endured a nomadic career, bouncing around the lower reaches of the Premier League on loan spells at Fulham and Leicester after being discarded by RB Leipzig.
But Lookman has found a home in Bergamo, where he will now forever be a hero.
"In the past few years I've been able to take my game to a new level and show that on a more consistent basis," said Lookman.
"I'm pleased with the progress I've made but this is just the beginning. I hope for more nights like this."
'Hurts for sure'
The 26-year-old's second goal was fit to win any final as he nutmegged Xhaka before curling a powerful shot into the far corner.
For the fourth time in seven Europa League knockout matches, Xabi Alonso's men found themselves 2-0 down.
Alonso has enjoyed a rapid rise to become one of Europe's hottest coaching properties.
The Spaniard has rejected the advances of former clubs Liverpool and Bayern Munich to remain at the BayArena next season.
However, Alonso's decision to start without a recognised striker did not work and he threw on Victor Boniface at half-time to give his side a focal point up front.
The damage, though, was already done as the German champions looked a side drained by their record run across three competitions.
"Normally it happens earlier but it is the first (defeat) in such a big game, it hurts for sure. We have to deal with this pain in a positive way," said Alonso.
"It didn't go as planned. We were not on our best level, so we will learn from today."
Atalanta were happy to soak up the Leverkusen pressure after the break and hit on the counter-attack.
The final blow was another fabulous finish from Lookman as he skipped past Edmond Tapsoba and this time blasted into the top corner on his weaker left foot.
Atalanta had lost all three of their previous finals under Gasperini, most recently in last week's Coppa Italia defeat to Juventus.
But this time they were not to be denied their shot at history as they were roared across the finishing line by the thousands clad in blue and black that had made the trip from northern Italy to the Irish capital.
In doing so they became the first Italian side to win the competition since Parma lifted the UEFA Cup in 1999.
