Heat the oil in a large skillet over medium-high heat. Brown the pork shoulder pieces in batches until they develop color on all sides, then transfer them to the slow cooker.
Add the onion to the same skillet and cook until it softens. Stir in the garlic, ginger, and red curry paste, cooking for one minute until fragrant.
Transfer the onion mixture to the slow cooker. Add the lentils, coconut milk, and chicken broth. Season lightly with salt and pepper, then stir to combine.
Cover and cook on low for 7 to 8 hours, until the pork is very tender and the lentils are soft.
Stir in the spinach during the last 10 minutes of cooking so it wilts into the stew.
Taste and adjust salt and pepper if needed. Serve hot with lime wedges on the side.