In a mixing bowl, combine the flour, dairy-free milk, vegetable oil, sugar, salt, and vanilla extract. Whisk until the batter is smooth and well combined. Let the batter rest for about 10 minutes.
In a separate bowl, prepare the filling by combining the dairy-free cream cheese alternative, sugar, lemon juice, vanilla extract, and dairy-free milk. Mix until smooth and creamy.
Heat a non-stick skillet or crepe pan over medium heat. Lightly grease the pan with dairy-free cooking spray or a small amount of oil.
Pour about ¼ cup of the batter into the pan, swirling it around to create a thin, even layer. Cook for about 1-2 minutes until the edges start to lift and the bottom is lightly golden. Flip the blintz and cook for an additional 30 seconds. Repeat with the remaining batter.
Once all the blintzes are cooked, spoon about 2 tablespoons of the filling onto the center of each blintz. Fold the sides over the filling, then fold the bottom up and roll tightly to enclose the filling.
Return the filled blintzes to the skillet, seam side down, and cook for another 1-2 minutes on each side until golden brown and heated through.
Serve the dairy-free blintzes warm, dusted with powdered sugar or drizzled with maple syrup, if desired.