When a guest books directly on your Lestis website, those dates are blocked immediately. The Lestis calendar is always live and up to date on its end.
Airbnb and Booking.com work by periodically reading ("polling") your Lestis calendar URL. They fetch it on their own schedule — typically a few times per hour for active properties. When they read it, they block the dates in their own system automatically.
The reverse also works: Lestis reads Airbnb's and Booking.com's iCal feeds to add their bookings to your availability, so your direct booking page stays accurate.
This bidirectional iCal setup is not a Lestis workaround. It is the standard the entire short-term rental world runs on, from small tools to large enterprise software.