Heat a large pot over medium-high heat. Coat the bottom with olive oil. once hot, add the onion celery and garlic and cook, stirring until softened, 2 to 3 minutes. Add half the dill and about a teaspoon of salt. Cook, stirring until fragrant, 1 to 2 minutes.
Add the pearl barley, stock, coconut milk, chick peas and kale and bring to the boil. Cover, reduce heat to medium-low and simmer, stirring occasionally, until the barley is swollen and tender, 25 to 30 minutes.
Turn off the heat. Add the lemon juice, and season with salt and pepper. Taste and make sure the seasonings are to your liking, adjusting salt and lemon as needed.