Your method will probably be effective - check out the aluminum foil covers many people use for their yeast starters. The theory is that bacteria, like dust, are carried by air currents/breezes/winds and settle with gravity. Bacteria can't "crawl" into your fermenter, so if the top is covered, you are mostly protected.
Playing devil's advocate to my own advice - yeast starters typically ferment quickly and vigorously, off-gassing a lot, and never sitting for more than a few days with a loose cover. Depending on your setup, your fermenting beer may experience some temperature and environmental changes that allow air to pass out of and into the fermenter without a proper airlock installed. Specifically, if the air temperature in the head space cools down, it may create a slight negative pressure and begin "sucking" bacteria laden air into the fermenter. So there is some risk to using the lid as you describe.
Finally, airlocks or blow-off tube setups are recommended for all fermentation, kits and original recipes alike. It's not about the ingredients, it's about controlling the fermentation environment.