Loot Llamas can be found in the "Loot" tab in game.
There are multiple types of Llamas:
Mini Llama - Reward for mission completion on some missions.
Upgrade Llama - Standard Llama, has a chance to go Silver or Gold to reward more, and possibly better quality items
Event llama - Llamas that are specific to the current event, which contain special items that will only be found in the event Llamas.
Rotating Llama - This is a Llama option that will change every day, and are typically more expensive, but give specific groups of items. Some examples include:
Ranged Weapon Llama
Melee Weapon Llama
It’s a Trap Llama
There are also “Super” variations of some of the Llamas, which will guarantee to reward the player with at least 1 Epic or higher tier item. The rotating Llamas also typically have a limit to the number of them that you can buy while the Llama is available.