I have the lullaby shotgun level one but the vendor does not have the blueprints
Hello Desmon0305,
Thanks for reaching out!
In order to upgrade your Lullaby, you need to do a few things: 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. 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 :-)
Hope it helps!