App.js

import React, { Component } from "react";
import { FlatList, StyleSheet, Text, View } from "react-native";

export default class HttpExample extends Component {
  state = {
    data: []
  };

  componentWillMount() {
    this.fetchData();
  }

  fetchData = async () => {
    const response = await fetch("https://tiagoandre.com.br/horarios.json");
    const json = await response.json();
    this.setState({ data: json.terminalUtil });
  };

  render() {
    return (
      <View style={styles.container}>
        <Text> Semana </Text>
        <FlatList
          data={this.state.data}
          keyExtractor={(x, i) => i}
          renderItem={({ item }) =>
            <Text>
              {`${item.horario}`}
            </Text>
            }
        />

      
      </View>
    );
  }
}

const styles = StyleSheet.create({
  container: {
    marginTop: 15,
    flex: 1,
    justifyContent: "center",
    alignItems: "center",
    backgroundColor: "#F5FCFF"
  }
});

LaravelController.php

<?php

namespace App\Http\Controllers\Api;

use Illuminate\Http\Request;
use App\Http\Controllers\Controller;
Use App\Models\Horario;
use DB;

class HorarioController extends Controller
{
    public function index () 
    {
        //$horario = Horario::get();

        $horarioTerminalUtil = DB::table('horario')->where('localPartida', 'terminal')->where('dia', 'util')->get();
        $horarioTerminalSabado = DB::table('horario')->where('localPartida', 'terminal')->where('dia', 'sabado')->get();
        $horarioTerminalDomingo = DB::table('horario')->where('localPartida', 'terminal')->where('dia', 'domingo')->get();

        return response()->json(array([
            'terminalUtil' => $horarioTerminalUtil, 
            'terminalSabado' => $horarioTerminalSabado,
            'terminalDomingo' => $horarioTerminalDomingo
        ]));
       

    }
}