An identity \(p=q\) is hypersatisfied by a variety \({\mathcal V}\) whenever \({\mathcal V}\models \tau (p)=\tau (q)\) for every hypersubstitution \(\tau \) (a mapping substituting operation symbols by arbitrary terms of appropriate arity). Whenever \(p=q\) is hypersatisfied in \({\mathcal V}\), it is called a hyperidentity of \({\mathcal V}\). When the terms being substituted are restricted to a submonoid \(M\) of all the possible choices, \(p=q\) is called an \(M\)-hyperidentity. A variety \({\mathcal V}\) is \(M\)-solid if each identity of \({\mathcal V}\) is an \(M\)-hyperidentity. The authors examine varieties whose identities are lattice \(M\)-hyperidentities for all submonoids of the monoid of all lattice hypersubstitutions and describe several particular cases of \(M\) which generate noncommutative lattices.