Cut beef into strips, about 1 cm wide. Peel and finely chop garlic. Squeeze 3 tablespoons juice from lime. In a bowl, mix together garlic, 1 1/2 tablespoons lime juice, 1 tablespoon oil, the paprika and thyme.
Add meat to lime-garlic mixture and turn to coat. Marinate in the refrigerator for at least 1 hour. Meanwhile, rinse bell peppers, wipe dry, remove seeds and cut peppers into thin slices. Peel onions and cut into wedges.
Heat the remaining oil in a heavy pan over medium-high heat. Add onions and bell peppers. Cook, stirring frequently, until tender, about 20 minutes.
In a bowl, combine sour cream and remaining lime juice, then season with salt and pepper. Rinse cilantro, shake dry, pluck leaves and coarsely chop. Mix half with the sour cream.
Rinse tomato, wipe dry, cut into quarters and remove seeds, if desired. Slice tomato thinly. About 2 minutes before peppers and onions are finished cooking, add tomato to pan and cook until slightly softened. Heat tortillas in the oven or microwave until warmed through.
Heat a grill pan over hight heat. Add beef and cook until medium-rare, 3-4 minutes. Divide beef and vegetables among tortillas. Top with remaining cilantro, then roll up fajitas and serve immediately with cilantro-sour cream on the side.