  UTe$_2$ has recently been found to be a likely spin-triplet superconductor
that exhibits evidence for chiral Majorana edge states. A characteristic
structural feature of UTe$_2$ is inversion-symmetry related pairs of U atoms,
forming rungs of ladders. Here we show how each rung's two sublattice degrees
of freedom play a key role in understanding the electronic structure and the
origin of superconductivity. In particular, we show that DFT+$U$ calculations
generically reveal a topological band that originates from a band inversion
associated with $5f$ electrons residing on these rung sublattice degrees of
freedom. Furthermore, we show that a previously identified strong ferromagnetic
interaction within a U-U rung leads to a pseudospin-triplet superconducting
state that can account for a non-zero polar Kerr angle, observed magnetic
field-temperature phase diagrams, and nodal Weyl fermions. Our analysis may
also be relevant for other U-based superconductors.
