asynread2.py

import asyncio
from urllib.request import urlopen

async def produce_lines(filename, delay):
    try:
        with open(filename, 'r') as file:
            for line in file:
                yield line.rstrip('\n')
                await asyncio.sleep(delay)

    except FileNotFoundError:
        with open("poe1.txt", 'w', encoding='utf8') as file:
            file.write(
                (urlopen("http://www.gutenberg.org/dirs/2/1/4/2147/2147-8.txt")
                 .read()
                 .decode("iso8859")))
            print("Hi, I've downloaded the The Works of Edgar Allan Poe (Volume 1) for you.\nPlease, re-run this program, shall you..?")

async def print_lines(filename, delay):
    async for line in produce_lines(filename, delay):
        print(f'[{filename}]', line)


def main():
    loop = asyncio.get_event_loop()
    tasks = [asyncio.Task(print_lines("poe1.txt", 0.5)),
             asyncio.Task(print_lines("poe2.txt", 0.3)),
             asyncio.Task(print_lines("poe3.txt", 0.6)),
             asyncio.Task(print_lines("poe4.txt", 0.5)),
             asyncio.Task(print_lines("poe5.txt", 0.2))]

    loop.run_until_complete(asyncio.gather(*tasks))

main()

You will need download the Works of Edgar Allan Poe for this one:

wget http://sprunge.us/TJaN -O poe1.txt; wget http://sprunge.us/bgHW -O poe2.txt; wget http://sprunge.us/jeQh -O poe3.txt; wget http://sprunge.us/ciCP -O poe4.txt; wget http://sprunge.us/MICg -O poe5.txt