@cFlour "Not all 1500 people use the internet service at the same time, so the service providers buy less IP's than the number of clients."
You're suggesting they have 66% of the required number, though. Depending on the ISP and location I think they'd quickly get into trouble; there's a lot of always-on devices these days which would immediately fail if what you say is true!
"do lichess IP bans imply on the device or internet address?"
Did you read my last message? How can they ban your device, when they can't identify it from your other devices on the same IP address?