  We study the procedure of regularization in the context of the Lipschitz
version of de Rham calculus on metric simplicial complexes with bounded
geometry. It provides us with the machinery to handle the de Rham homomorphism
for $L_\pi$-cohomologies. In this respect, we obtain the condition resolving
the question of triviality of the kernel for de Rham homomorphism. In
particular, we specify the non-trivial cohomology classes explicitly for a
sequence of parameters $\pi = \langle p_0,\,p_1,\dots,\,p_n\rangle$ missing
non-increasing monotonicity.
