Add the chopped onion to a food processor and blend for 20-30 seconds, until almost pureed.
Add the cooked shrimp to the food processor and pulse 1-2 times until coarsely chopped.
Transfer the onion and shrimp mixture to a large bowl.
Add the softened cream cheese to the bowl and mix everything by hand or with a hand mixer until smooth and well combined.
Squeeze the lemon juice over the mixture and add garlic powder, onion powder, salt, and pepper. Mix thoroughly and taste to adjust seasoning.
If the dip is too thick, add milk 1 tablespoon at a time until the desired consistency is reached.
Serve with large corn chips and enjoy!