The lattice isomorphism problem (LIP) asks, given two lattices \(\varLambda _0\) and \(\varLambda _1\) , to decide whether there exists an orthogonal linear map from \(\varLambda _0\) to \(\varLambda _1\) . In this work, we show that the hardness of (a circular variant of) LIP implies the existence of a fully-homomorphic encryption scheme for all classical and quantum circuits. Prior to our work, LIP was only known to imply the existence of basic cryptographic primitives, such as public-key encryption or digital signatures.