Rinse rice a few times under cold running water until water runs clear.
Bring rice, water, and coconut water to a boil in a saucepan. Reduce heat to medium-low, cover, and simmer until rice is tender and water has been absorbed, 20 to 25 minutes.
Heat oil in a wok or large cast iron skillet over medium heat. Add shallot and cook until softened, about 3 minutes. Add garlic and cook until fragrant, about 30 seconds. Add red bell pepper, ginger, and lemongrass. Allow to cook for 3 to 5 minutes. Add curry paste and mix until well combined. Add cooked rice and mix well. Move rice mixture to one side of the wok and crack eggs into the wok. Cook and stir eggs until set and scrambled, about 3 minutes. Mix scrambled egg with rice mixture. Add frozen vegetables and mix well. Stir in coconut milk.