Place the onion, garlic, celery, and asparagus in a large dutch oven, and cover with 2 cups of the vegetable broth. Bring to a boil. Once boiling, cover and simmer for 10 minutes until vegetables are tender.

Remove vegetables and broth from heat and puree. Transfer puree to a separate bowl.

Add in the remaining 2 cups of vegetable broth, mix, and bring to a boil. Once boiling, add the puree back in, and mix well, pureeing all together again.

Mix the cornstarch with 1/4 cup water. Pour mixture into soup, mix well, and let cook for 2 minutes to thicken.

Add in the coconut milk, lemon juice, and salt and pepper, and mix well. Heat for 5 more minutes and serve.