Combine tomatoes, cilantro, and lime juice in a small bowl; set aside.
Place black beans in a small microwave-safe dish; partially mash beans with a fork. Cover and microwave at HIGH 2 minutes.
Melt butter in a large nonstick skillet. Add eggs; cook over medium-high heat 1 to 2 minutes on each side or until done (do not break yolks).
Warm tortillas according to package directions. Spread beans evenly over tortillas; top each with 1 egg. Top with tomato mixture and cheese