I am pretty sure that from a bear's point of view a llama counts as food, but as its not possible to put a llama into a bear can or suspend it from a tree branch, how would I keep it from being eaten on a backpacking trip?
Why bring only one llama? If one is fun two are twice as nice!
In all seriousness llamas are herd animals so they would probably be better protected as a group since this is their standard defensive tactic in the wild.
Alternatively/additionally you can bring a dog with you too. The dog will help prevent predators from attacking the llama(s) which is one of the reasons why shepherds had dogs.
llamas are only native to an area of South American unless you are hiking in that area, they are not going to be any more of a prospective meal then then the other animals on the hike (i.e. humans). They are human sized or bigger (a full-size llama is 1.7 to 1.8 m (5.6 to 5.9 ft) tall at the top of the head, and can weigh between 130 and 200 kg (290 and 440 lb).).
If a bear comes looking for a meal in your camp, and chooses to try eating the llama instead of you, it is your lucky day. Heck even if the bear decides you are the meal, your llama might protect you
In short, the llama is less likely to be the bears meal then you are. Take the precautions from What precautions should I take to protect myself and my camp from bears? and you should both be safe.
Not limited to bear. A mountain lion, wolf, or coyote may attack you or domestic animals.
Even on your property with a fence bear may attack domestic animals including llama.
Not practical to take a bear proof fence backpacking.
Bear repellent but if you defend the llama you introduce yourself as a possible target. A gun but be aware it takes a big gun to drop a bear. And a bear attack is more likely at night so have a light on the gun. But you have a llama to carry the big gun. The llama will most likely sense danger and give you warning.
Where are you going? If guides are using llama in the area then ask them. If guides are using llama in the area period it is probably safe. In aggressive bear county I would look for country where bears are not aggressive.
In high country like above tree line bear attack is not common. That is the natural habitat of llama and clearly they have survived.
A llama is pretty fast and very agile. Without a pack it can probably elude a bear. Just release the llama.
Question was edited to pack animal after I answered. My answer would be different for a horse. A bear is less likely to attack prey as big as a horse. A horse is better at defending itself. And a horse can out run a bear.
I've seen a number of people llama packing in black bear territory in the Sierras. Typically the llamas are hobbled or tied to a line; they can still kick and spit, and they can make noise. Most bears are afraid of humans and domestic animals; the ones that aren't rapidly get shot and/or relocated. Even so, a bear would certainly prefer a poorly guarded gorp cache (or the feed of the llama) to a large angry domestic animal, so, in practice, it isn't necessary to take special precautions for llamas, or horses for that matter.
Mountain lions may be a different case, but I haven't seen too many llama packers in mountain lion territory.
There are a lot of different types of bears. Protecting a llama from a giant panda should be quite easy as you are unlikely to see one in the wild and their diet is almost entirely bamboo. If you are in polar bear territory, you should probably be more worried as they are natural hunters, curious, and powerful. That said, I am not sure a llama is a good choice for an arctic pack animal.
The American black bear predominately eat vegetation, although when food sources are scare they have been known to prey on large animals (e.g., horse and cattle), but prefer to prey on smaller animals. Outside of early spring, there is probably little risk to a llama.
The grizzly bear again predominately eats vegetation, but will attack large animals. Again, they prefer to prey on smaller animals. A hungry grizzly definitely presents a risk to a llama, but also presents a risk to you.