Heat a medium pot over medium-high heat, 2 minutes. Add oil, then stir in onion and garlic. Cook, stirring often, until onion is translucent, about 4 minutes.
Pour in bulgur and stir to coat with oil. Add broth. Let mixture come to a boil, then stir in spinach, cover, and reduce heat to simmer. Cook until all liquid has been absorbed and bulgur is tender, about 20 minutes. Season with salt and lemon juice.