Karim Adeyemi opened the scoring for the hosts in the 22nd minute, but Hakon Haraldsson equalised for the French side in the 68th minute after a well-placed assist from Jonathan David.
Dortmund dominated the first half, showing the attacking intensity expected of them at home.
However, they struggled to maintain their grip on the match in the second half, allowing Lille to grow in confidence and find their way back into the game.
Captain Emre Can admitted the team lacked the resilience needed to secure victory, stating they failed to "push past the pain barrier."
"The second half was not good at all. Too little intensity off the ball and too little ball possession," Can told Amazon Prime.
"We didn't push past the pain barrier - and that's what you need to do against Lille. They're a good team - they're here in the last 16 for a reason.
"We need to be more courageous - it wasn't good enough today. We can do better and we will."
This result adds to what has been a difficult season for Dortmund. The German side sit 10th in the Bundesliga and were eliminated from the German Cup in the second round, marking an overall underwhelming campaign.
In an effort to turn things around, Dortmund appointed Niko Kovac as manager in January.
His arrival has sparked some improvement, with the team keeping four clean sheets in their last six matches and securing back-to-back league wins for the first time this season.