What do you mean by "the cloud based LR", Kevin? I'm not being awkward but Adobe haven't helped us with their product naming! Do you mean the one-year-old Mac/PC application that Adobe call "Lightroom CC"? Update: I'll assume so. I'm also unclear what you mean by "your library". The photos, or what Lightroom calls the catalogue?
Anyway "Lightroom CC" is a bit like Lightroom Mobile but running on your laptop. It can work offline, syncing later, but it is really designed to work best online. So when I last played with it, you couldn't even search or filter your photos without being online. Although it has a local cache, its catalogue is in the cloud and you can't back it up locally.
But Lightroom has a variety of cloud features, not just "Lightroom CC", and you can pick and choose. "Cloud-based" is really cloud-dependent, and you do need good internet connections, not just decent, before it becomes viable.