Martin Stranzl's penalty put the Bundesliga side ahead before Sergio Floccari and Libor Kozak turned the pendulum Lazio's way.
Stranzl then missed his second penalty, which also saw Andre Dias dismissed following his second yellow card, before three goals in six minutes brought a pulsating 3-3 draw to an end.
Atletico Madrid look to be heading out after they were beaten 2-0 at home by Rubin Kazan. Gokdeniz Karadeniz put the Russians ahead after six minutes before Pablo Orbaiz doubled their advantage in added on time.
Juande Ramos' chances of becoming only the second manager to win the Europa League for a third time may have to wait another year after his Dnipro side were beaten 2-0 by Basle at St. Jakob-Park.
However a first-half goal from Valentin Stocker and a second-half strike from Marco Streller ensured the Swiss side head into next week's second leg at the Dnipro Stadium in control.
A last-minute goal from Glynor Plet gave Genk a precious away goal as they held Stuttgart 1-1 at the Mercedes-Benz Arena.
Christian Gentner had fired the hosts ahead before half-time, but Plet struck in stoppage time to level the scores and give his team the advantage heading into the return match in Belgium next week.
Rodrigo Palacio scored twice following his early entrance as a substitute to put Inter Milan in control of their tie against Cluj.
Palacio, a 10th-minute replacement after a serious-looking injury to Diego Milito, scored 10 minutes after that and added a late second in a 2-0 win.