On cubature formulas exact for Haar polynomials in the case of two-variable functions satisfying the general Lipschitz condition

A number of upper error estimates are obtained for the cubature formulas possessing the Haar $d$-property in the case of two-variable functions belonging to the $\operatorname{Lip}(L_1,L_2)$ classes and satisfying the general Lipschitz condition. It is shown that, on the classes under consideration, the errors of the minimal cubature formulas possessing the Haar $d$-property have the best convergence rate to zero.