Technically no and yes. It depends on which choice you pick when Creating the Work. There's a private (you only), Lulu Marketplace (just Lulu.com), and then the larger Marketplace (gives your book an official ISBN for free, puts it on Amazon, Barnes & Noble and other sites they're affiliated with). However this is strictly only if your book can be made with Amazon/ect's work. My novels specifically are a measurement size that isn't "standard" in the eyes of Amazon, so I've been blocked from releasing on their site for literal years. The closest size they have available is too small, or too large, for my purposes, and Amazon's Createspace specifically charges (for my book) about $5 more to be sold on their marketplace.
Here they talk in their ToS specifically about how they utilize the publishing platforms of sites like Amazon, without specifically naming Amazon or other shops since affiliations can change.
http://www.lulu.com/about/legal#thirdParty