Is it hard to build muscle on a vegetarian diet?

Depending on how strict of a vegetarian you are, there are still plenty of ways to get protein from your diet. The key will be getting complete proteins and also important is keeping up your energy levels so you can make it through the workout.

If you are not a very strict vegetarian, you can just eat fish and seafood and you will be fine for protein.

If you are choosing not to eat fish, then you still have things like nuts, beans, legumes and eggs which are also great sources of protein. It is definitely possible to build muscle from these sources of protein. One important thing to remember when eating vegetarian is to balance your omega 3’s and omega 6’s. Try using flax or chia seeds to help with this.

Some vegetarians rely on fortified protein drinks or snacks, which are all right, but a very strict vegetarian will need to consider the source. What ingredients are being used to fortify these foods? Some of these drinks and snacks will conflict with some vegetarians’ beliefs.

To think of it more philosophically, consider that many of the animals we eat get their protein from the earth. Think about how we eat cows, pigs, chickens, etc. These animals are fed grains, corn and soy mostly. So it is definitely possible to get protein from sources that aren't animals. Even in nature we are genetically closest to primates such as chimpanzees, monkeys, gorillas, etc. These primates are largely not meat eaters. Gorillas have plenty of muscle and their primary diet is bamboo, fruits and stems.

As for your workout, as long as you maintain good energy levels (have a good sleep routine, avoid stress, and eat a complete and balanced diet), and you eat lots of vegetables, then you should be able to make it through your workout just fine. And as for protein, if you eat a diet rich with natural sources of protein you will likely be getting a complete diet of all the essential amino acids (proteins).

Google: “best sources of vegetarian protein” or something very similar and find some foods you really like. Don't be afraid to experiment a little with new foods too.