Give Eridium to Lilith is an objective in the Story Mission, Paradise Found in Borderlands 2: Commander Lilith and the Fight For Sanctuary
- RUn back to Crimson Plaza and approach Lilith.
- Simply interact with her to give her the needed Eridium.
- Watch the ending cutscene.
- When it ends, you are taken to the Backburner.
- Head into Vaughn's Headquarters and approach Lilith to complete and turn in the quest.