The rumored new DLC for BL2 that aims to fill in the gap between this game and BL3 is now out on Steam and free (until July 8th) for all owners of BL2!

From the Steam page:

Commander Lilith & the Fight for Sanctuary will be available for free to all owners of Borderlands 2 and Borderlands: The Handsome Collection until July 8 at 06:59:59 UTC (11:59:59 PDT). Requires Borderlands 2 or Borderlands: The Handsome Collection to play.

It has even got a trailer:

Borderlands 2: Commander Lilith & the Fight for Sanctuary Official Trailer

Key features:

• NEW STORY Join Lilith and step back into the boots of legendary Vault Hunters Maya, Salvador, Axton, Zer0, Gaige or Krieg to take down a deranged villain hell-bent on ruling Pandora.
• NEW LOOT Go beyond legendary with the brand new Effervescent loot tier.
• NEW LEVEL-CAP Returning players can pursue an increased level cap of 80, while newcomers can automatically boost to level 30 and dive right into the action.