We study chiral-odd quark-antiquark correlation functions suitable for lattice calculations of twist-three nucleon parton distribution functions h(L)(x) and e(x), and also the twist-two transversity distribution delta q(x). The corresponding factorized expressions are derived in terms of the twist-two and twist-three collinear distributions to one-loop accuracy. The results are presented both in position space, as the factorization theorem for Ioffe-time distributions, and in momentum space, for quasi- and pseudo-distributions. We demonstrate that the twist-two part of the h(L) quasi(pseudo)-distribution can be separated from the twist-three part by virtue of an exact Jaffe-Ji-like relation.