In a medium-sized bowl, mix together the drained tuna, mashed avocado, mayonnaise or Greek yogurt, lemon juice, red onion, and cilantro. Season with salt and pepper to taste.
Lay the tortillas or wraps on a clean surface. Spread an even layer of the tuna-avocado mixture onto each tortilla, leaving about an inch border around the edges.
Top each tortilla with a layer of spinach leaves, followed by cucumber slices and shredded carrots.
Roll up each tortilla tightly, tucking in the sides as you go, to create a wrap. Cut each wrap in half diagonally to serve.