  We present the first $L-$band (2.8 to 4.1~$\mu$m) spectroscopy of
$\kappa$~Andromedae~b, a $\sim20~M_{\mathrm{Jup}}$ companion orbiting at
$1^{\prime\prime}$ projected separation from its B9-type stellar host. We
combine our Large Binocular Telescope ALES integral field spectrograph data
with measurements from other instruments to analyze the atmosphere and physical
characteristics of $\kappa$~And~b. We report a discrepancy of $\sim20\%$
($2\sigma$) in the $L^{\prime}$ flux of $\kappa$~And~b when comparing to
previously published values. We add an additional $L^{\prime}$ constraint using
an unpublished imaging dataset collected in 2013 using LBTI/LMIRCam, the
instrument in which the ALES module has been built. The LMIRCam measurement is
consistent with the ALES measurement, both suggesting a fainter $L$-band
scaling than previous studies. The data, assuming the flux scaling measured by
ALES and LMIRCam imaging, are well fit by an L3-type brown dwarf. Atmospheric
model fits to measurements spanning 0.9-4.8~$\mu$m reveal some tension with the
predictions of evolutionary models, but the proper choice of cloud parameters
can provide some relief. In particular, models with clouds extending to
very-low pressures composed of grains $\leq1~\mu$m appear to be necessary. If
the brighter $L^{\prime}$ photometry is accurate, there is a hint that
sub-solar metallicity may be required.
