The Belgium striker was quoted last week outlining his desire to leave Everton for a "top club" in the future, but his commitment to his current employers could not be questioned in a devastating display at the Stade de Suisse on Thursday.
In an opening quarter largely dominated by the visiting team, it was the hosts who went ahead through Guillaume Hoarau's impressive curled effort.
But Everton had always looked comfortable on the artificial surface - despite manager Roberto Martinez's pre-match concerns - and hit back through quickfire Lukaku and Seamus Coleman goals midway through the first half.
Another from Lukaku put Martinez's men in the driving seat and he completed his treble - his first for the club - with a neatly taken strike in the second half.
Hoarau missed a penalty soon after, while John Stones was dismissed in giving the spot-kick away.
But it mattered little as Young Boys' seven-match winning streak in home European games was snapped, putting Martinez's side in firm control of the tie.
Undaunted by their hosts' impressive home form, Everton twice went close early on, but Hoarau made them pay for slack marking with nine minutes gone when, left in the clear 25 yards out, he despatched with ease beyond Tim Howard.
Lukaku and Ross Barkley tested Yvon Mvogo in Young Boys' goal, before the Belgian deservedly levelled the scores.
Gareth Barry measured a left-wing cross, allowing Lukaku to hold off his marker and guide an accurate header in at the near post.
The game was turned on its head just four minutes later as intricate build-up play got Steven Naismith to the byline and the Scot's drilled cross went through Mvogo, leaving Coleman to tap in on the stretch.
Hoarau tested Howard with a volley and flashed a header wide, but Young Boys were caught on the counter as Everton took control after 39 minutes - Lukaku converting into an unguarded net after Barry's centre fell kindly.
A breathless first half ended with James McCarthy clearing Sekou Sanogo's effort off the line and the midfielder was perhaps lucky to only see a yellow card for a clash with Barkley shortly after the interval.
Everton were happy to sit on their two-goal lead, but another counter-attack reaped rewards three minutes before the hour as Lukaku raced clear on the end of Barkley's throughball and dinked over the onrushing Mvogo.
Young Boys had a chance to reduce the deficit as Stones hauled Hoarau down inside the area - earning a red card - but the Frenchman's languid effort was blazed into the stand.
The hosts threw striker Alexander Gerndt on in an attempt to salvage something from the contest, but they will need a footballing miracle to progress when the sides meet at Goodison Park next week.
