Wallhaven is a wallpapers website we use to source images. "Wallpapers lite", ultimately, is just a proxy. To get you access to the images we use official Wallhaven API, which is limited to 45 requests per minute.
It wouldn't be a problem, if Wallhaven allowed us to make requests directly from a browser. This way the limit would apply per user only. However, currently Wallhaven prevents such requests by not providing CORS headers.
The only available option is to use a server-side proxy, which is exactly how "Wallpapers lite" works right now. Unfortunately, it means the 45 requests per minute limit applies to all users, not just individual ones.
For example, if 90 users open a page roughly at the same time, it will send 90 requests to Wallhaven and Wallhaven will block half of them due to its API rate limiting.
It's frustrating, but there is nothing we can do about it. It is also understandable why Wallhaven set such restrictions, so we can't just demand to lift them.
Currently, the only solution is to wait and try again whenever you encounter such an error.