In a food processor fitted with a metal blade, process carrots until broken down into a paste, transfer to deep mixing bowl.
Add lemon juice, olive oil, parsley, red onion, salt and liquid smoke and mix until all ingredients are well combined,
In a clean bowl, add cream cheese and process until smooth, about 30 to 45 seconds. Use a rubber spatula to scrape down the sides of the machine.
Lay one wrap on a flat surface. In the middle of the wrap, spread 1/4 of the cream cheese mixture into the middle, leaving about 1/4-inch of space on both ends. Top the cream cheese with 1/4 of the carrot lox mixture, and about 1/2 cup of lettuce. Starting from the bottom of the wrap, roll up wrap around filling until tight. Repeat process with remaining wraps and ingredients.
Place wraps seal down in a container and refrigerate to help cream cheese firm and set, about 1 hour.
Remove wraps from fridge and cut into slices approximately 12-inch thick. Serve immediately or store refrigerated for up to 5 days.