The requests give them "this IP address just loaded a page on Lyra", which gives them the ability to keep track of which IP addresses are using your site, how m

The requests give them "this IP address just loaded a page on Lyra", which gives them the ability to keep track of which IP addresses are using your site, how many pages they're loading on it, how long they're spending on the site, and so on. With their other data, they'd often be able to associate an IP and those requests with a specific person. Again, maybe this isn't a level of privacy-loss that you're concerned about, but it's just not compatible with promising that you aren't giving away "a single bit" of user data.