  Focusing on the recently-discovered candidate topological insulator
$\alpha$-(BEDT-TSeF)$_2$I$_3$ -- having two-dimensional charge-neutral Dirac
cones in a low symmetry lattice -- we combine ab-initio and extended-Hubbard
model calculations to deal with spin-orbit and non-local repulsive
interactions, and find a realization of an interaction-induced quantum spin
Hall (QSH) insulator, similar to the one proposed in the honeycomb lattice
under next-nearest neighbor repulsions. In the absence of repulsive
interactions, a topological insulator appears by the spin-orbit coupling and is
characterized by a nonzero spin Chern number. By considering up to next-nearest
neighbor repulsions at Hartree-Fock level, the intrinsic spin-orbit gap is
found to grow by orders of magnitude and a QSH insulating phase appears that
has both a finite spin Chern number and order parameter. Transport coefficients
and spin susceptibility are calculated and found to consistently account for
most of the experimental findings, including the metal-to-insulator crossover
occurring at $\sim50$ K as well as the Berry phase change from 0 to $\pi$ under
hydrostatic pressure. We argue that such a QSH insulating phase does not
necessitate a sizeable spin-orbit interaction to generate a large insulating
gap, which is highly advantageous for the search of novel topological phases in
generic materials having low symmetry lattice and/or small spin-orbit coupling.
