Combine the parsley and cilantro (leaves and stems), garlic, half of the sliced onion, 1 tablespoon salt, 1 teaspoon pepper, vinegar, 2 tablespoons lemon juice and 1/2 cup olive oil in a food processor; blend into a thick and smooth chimichurri sauce. Pierce both sides of the steak with a fork several times; place in a resealable plastic bag and add half of the sauce. Seal the bag and turn to coat the steak; refrigerate for at least 1 hour. Cover and reserve the remaining sauce.
Preheat a grill to medium-high. Remove the steak from the bag (discard the bag of sauce); season with salt and pepper and grill until medium-rare, about 6 minutes per side. Let rest, loosely covered with foil, for 10 minutes.
Meanwhile, heat the remaining 1 tablespoon olive oil in a large skillet over medium-high heat. Add the peppers and the remaining sliced onion half; season with salt and pepper. Saute until the vegetables are softened and caramelized around the edges, about 8 minutes. Add the beer, cover and cook until the peppers are tender, about 5 minutes.
Warm the tortillas on the grill. Thinly slice the steak on the bias; divide among the tortillas along with the peppers and onions. Thin the reserved chimichurri sauce with the remaining 1 tablespoon lemon juice; drizzle over the fajitas. Serve with lime wedges, if desired.