We present a data-driven method to estimate absolute magnitudes for O- and B-type stars from the LAMOST spectra, which we combine with {it Gaia} parallaxes to infer distance and binarity. The method applies a neural network model trained on stars with precise {it Gaia} parallax to the spectra and predicts $K_{rm s}$-band absolute magnitudes $M_{Ks}$ with a precision of 0.25,mag, which corresponds to a precision of 12% in spectroscopic distance. For distant stars (e.g. $>5$,kpc), the inclusion of constraints from spectroscopic $M_{Ks}$ significantly improves the distance estimates compared to inferences from {it Gaia} parallax alone. Our method accommodates for emission line stars by first identifying them via PCA reconstructions and then treating them separately for the $M_{Ks}$ estimation. We also take into account unresolved binary/multiple stars, which we identify through deviations in the spectroscopic $M_{Ks}$ from the geometric $M_{Ks}$ inferred from {it Gaia} parallax. This method of binary identification is particularly efficient for unresolved binaries with near equal-mass components and thus provides an useful supplementary way to identify unresolved binary or multiple-star systems. We present a catalog of spectroscopic $M_{Ks}$, extinction, distance, flags for emission lines, and binary classification for 16,002 OB stars from LAMOST DR5. As an illustration of the method, we determine the $M_{Ks}$ and distance to the enigmatic LB-1 system, where Liu et al. (2019) had argued for the presence of a black hole and incorrect parallax measurement, and we do not find evidence for errorneous {it Gaia} parallax.
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