The authors consider weak type inequalities, involving two weight functions, for potential operators acting on Lorentz spaces. The underlying metric on \(R^ n\) is defined in terms of the quasi-norm \[ \| x\|=\max_{i=1,\dots,n}| x_ i|^{\alpha_ i},\;\alpha_ i>0\text{ and } \sum_{i=1}^ n \alpha_ i=n. \] The necessary and sufficient condition on the weights is analogous to the one studied earlier by E. Sawyer [Trans. Am. Math. Soc. 281, 339-345 (1984; Zbl 0539.42008)].