  We report on a high-resolution spectroscopic survey of
${}^{6}\textrm{Li}{}^{40}\textrm{K}$ molecules near the
$2\textrm{S}+4\textrm{P}$ dissociation threshold and produce a fully empirical
representation for the $\textrm{B}^{1}\Pi$ potential by connecting available
short- and long-range data. The purpose is to identify a suitable intermediate
state for a coherent Raman transfer to the absolute ground state, and the
creation of a molecular gas with dipolar interactions. Starting from weakly
bound ultracold Feshbach molecules, the transition frequencies to twenty-six
vibrational states are determined. Our data are combined with long-range
measurements [Ridinger et al., EPL, 2011, 96, 33001], and near-dissociation
expansions for the spin-orbit coupled potentials are fitted to extract the
$C_6$ dispersion coefficients. A suitable vibrational level is identified by
resolving its Zeeman structure and by comparing the experimentally attained
g-factor to our theoretical prediction. Using mass-scaling of the short-range
data for the $\textrm{B}^{1}\Pi$ [Pashov et al., Chem. Phys. Lett., 1998, 292,
615-620] and an updated value for its depth, we model the short- and the
long-range data simultaneously and produce a Rydberg-Klein-Rees curve covering
the entire range.
