Add your feta, cream cheese, heavy cream, olive oil, and garlic clove to the blender or food processor. Pulse over and over in short bursts, wiping down the sides of the blender when needed. If it looks like it needs more liquid, add more heavy cream or olive oil.

When the dip is well combined, add the lemon juice, lemon zest, and fresh dill. Season with salt and pepper to your preference, then continue pulsing until entire mixture is smooth.