The Lullaby Exotic Shotgun is a pre-order bonus for The Division 2, and currently cannot be gotten from random drops in the game. As you get deeper into the game, however, it loses its power and needs to be left behind. The good news is, it can be upgraded to make it more relevant in the late game!
How To Upgrade The Lullaby Exotic Shotgun
Once you reach Level 30, the game starts to worry less about the level or a weapon, and more about its Gear Score. This is also the time that you can upgrade your Exotic weapons! To do this, head for the Crafting Bench in the White House.
Go into the Weapon section and scroll down until you come to the Exotics. As long as you pre-ordered the game, you should see an option there called Lullaby Upgrade. Now, this is the interesting bit. To upgrade the Lullaby, you need to use a Sweet Dreams Exotic Shotgun to do so. The Sweet Dreams can drop from named Outcast enemies. You will also need materials like Steel, Titanium, and Receiver Components, so make sure you have enough of them before you try to upgrade.
Once you have all the components and the Sweet Dreams, you will be able to upgrade the Lullaby Exotic Shotgun to a Gear Score that makes it far more relevant for where you are in the game.
I hope this guide helps, as there seems to be a little bit of confusion about what you need to upgrade the Lullaby Exotic Shotgun. Remember, another Sweet Dreams Shotgun can always drop for you, where an upgrade Lullaby Exotic Shotgun will never drop. As such, it is an upgrade worth making.