Besiktas made a bright start amid a raucous atmosphere but the home fans were nearly silenced in the 14th minute, when Corentin Tolisso broke into the box and controlled Lacazette's pass but could only fire wide.
Lyon held their nerve in the shootout to emerge 7-6 victors at the Vodafone Arena after the second leg finished 2-1 in favour of Besiktas, to level the aggregate score at 3-3.
Dusan Tosic saw his spot-kick parried by Anthony Lopes, but Jallet ballooned the decisive effort over the bar.
But on number eight, Matej Mitrovic's effort was saved for Besiktas and Maxime Gonalons then made no mistake to put Lyon through and plunge the Turks into despair.
UEFA said in a statement Wednesday that both clubs would be excluded from the next competition for which they qualified - with the ban being deferred for a probationary period of two years.
President Jean-Michel Aulas praised the response to last week's crowd trouble, while stopping short of confirming whether Lyon had accepted the sanctions, or planned to contest them.
The tension was on the pitch rather than the stands as both sides scrapped energetically for the semi-final berth.
"This qualification isn't only about focus and the mental aspects, it also hinges on technical and tactical matters", said Genesio, who could hand Maxwel Cornet a start on the right of attacking midfield instead of Rachid Ghezzal, and who feels that his team have what it takes to come out on top in Turkey despite Besiktas' first-leg away goal.
Lacazette almost put the game beyond Besiktas' reach after the break, hitting the woodwork with a pearl of a shot and watching the ball cross across the goal.
Earlier, Talisca had scored either side of a strike from Alexandre Lacazette to level the tie on aggregate.
There was a huge let-off for Lyon five minutes from time as Lopes misjudged Ricardo Quaresma's cross, which rebounded back off the post into the path of Ryan Babel, who could only hack a shot wildly into his team-mate Tosun. For Lyon, Lacazette hit the crossbar. Fabricio denied Lyon's Corentin Tolisso with a spectacular one handed save.
UEFA announce that Lyon and Besiktas will be banned from European competitions if last week's violent scenes are repeated.
The November 1993 clash between Istanbul's Galatasaray and Manchester United - when Turkish fans welcomed the English team with "Welcome to Hell" banners - is still remembered but Turkish football bosses like to think fan behaviour has moved on since then.