LWE and SIS-based cryptography absolutely <i>is</i> lattice-based crypto, and I can&#x27;t really imagine what other kind of scheme you would deem more deserving of the name than those. Even the epitome of classical lattice-based crypto, Ajtai-Dwork, is proved secure under a problem (hidden hyperplane) which is &quot;not actually a lattice problem itself&quot;, at least not anymore than LWE and SIS. But being based on a problem equivalent to worst-case lattice problems under polynomial-time reductions strikes me as the strongest possible sense in which you could claim a scheme to be lattice-based.