"Do I look bloated to you?"
While using a home pregnancy test on a giant lizard is bad science, and calling a lizard that lays eggs "pregnant" bad grammar (the correct term is gravid), the idea of an animal reproducing without a mate is not only possible, but occurs in many species. An example of such lives at Briar Bush Nature Center, and is called the Vietnamese walking stick.
In the wild, Vietnamese walking sticks do reproduce sexually, with males and females, but when you are a small insect in a large rainforest, a mate can be hard to come by, especially when your lifespan is a short 8 months. (And you thought your mother pressuring you to find a spouse in 22 years was rough.) In the absence of a male, female walking sticks are able to reproduce by parthenogenesis; they lay unfertilized eggs that develop into clones of the female. Although this kind of reproduction does not allow for adaptations to changing conditions in the environment, it does allow the female to reproduce and give her bloodline a little bit longer to find a mate.
In captivity, there are no male Vietnamese walking sticks! Every single walking stick you'll see is a female. Thanks to parthenogenesis, it's easy for me to keep my population of walking sticks going. Once a female has reached about 6 months of age, she starts laying eggs, and then 2-4 months later, an adorable little clone emerges.
*singing* "My Little Cloney, sweet little cloney..."
The only part of the Vietnamese walking stick life cycle that I have a hard time with is raising the eggs. They need just the right humidity in order to hatch. In order to monitor the eggs every day, I raise them in my house, in a little plastic container. The majority don't hatch, but when each female lays 20-40 eggs, that's not a bad thing. On the days that an egg hatches, it's like waking up to Christmas morning. A baby walking stick has magically appeared in the container! Squeeeeee! And in just 6 months, that little Vietnamese walking stick nymph little will lay her own eggs and the cycle will begin all over again, no pregnancy test needed.