Heat the oil in a large pot over medium heat. Add the onion, garlic, and ginger and cook for 3 minutes until the onion softens.
Stir in the rinsed lentils, vegetable broth, coconut milk, and bruised lemongrass pieces. Bring the mixture to a gentle boil, then reduce heat and simmer uncovered for 25 minutes, stirring occasionally.
Remove the lemongrass stalks. Add the chopped bok choy and soy sauce. Simmer for 5 more minutes until the bok choy wilts but still holds some texture.
Turn off the heat. Stir in the lime juice and season with salt and pepper. Sprinkle with chopped cilantro before serving.