The purpose of this note is to extend previous results of V. Blomer and the author in [Math. Proc. Camb. Philos. Soc. 159, 239–252 (2015; doi:10.1017/S030500411500033X)] to encompass nonclassical quadratic forms (that is, forms with odd cross coefficients), as well as to strengthen some of the statements in that paper and to simplify the proofs. In fact, the arguments in the present paper apply also to the case of nonfree quadratic \(\mathcal O_K\)-lattices, where \(\mathcal O_K\) denotes the ring of integers of a real quadratic field \(K=\mathbb Q(\sqrt{D})\). In this general context, the main result of the paper is the following: For each positive integer \(M\), there are infinitely many real quadratic fields \(K=\mathbb Q(\sqrt{D})\) which do not admit totally positive integral universal \(\mathcal O_K\)-lattices of rank \(M\).