Let \(Q\) be a quasivariety of lattices. Denote by \(\text{Int}(Q)\) the quasivariety of lattices generated by interval lattices of all members of \(Q\). A lattice quasivariety is called proper if it does not coincide with the variety of all lattices.
Theorem 1. If \(Q\) is a proper quasivariety of lattices then \(\text{Int}(Q)\) is also a proper quasivariety.
Theorem 2. There exists an uncountable set of lattice quasivarieties \(Q\) such that \(\text{Int}(Q)=Q\).