Heat 1/4 cup oil in heavy large skillet over medium-high heat. Working in batches, fry tortilla strips until golden, about 2 minutes. Transfer to paper towels. Sprinkle with salt. Whisk lime juice, shallot, and honey in small bowl. Whisk in 3 tablespoons oil. Season with salt and pepper. DO AHEAD Can be made 1 day ahead. Cool strips completely and store in airtight container at room temperature. Cover and chill dressing. Place mache and avocado in large bowl. Add dressing; toss. Season with salt and pepper. Top with tortilla strips.