  Three Luminous Blue Variables (LBVs) are located in and near the Quintuplet
Cluster at the Galactic Center: the Pistol star, G0.120-0.048, and qF362. We
present imaging at 19, 25, 31, and 37 {\mu}m of the region containing these
three LBVs, obtained with SOFIA using FORCAST. We argue that the Pistol and
G0.120-0.048 are identical ``twins" that exhibit contrasting nebulae due to the
external influence of their different environments. Our images reveal the
asymmetric, compressed shell of hot dust surrounding the Pistol Star and
provide the first detection of the thermal emission from the symmetric, hot
dust envelope surrounding G0.120-0.048. Dust and gas composing the Pistol
nebula are primarily heated and ionized by the nearby Quintuplet Cluster stars.
The northern region of the Pistol nebula is decelerated due to the interaction
with the high-velocity (2000 km/s) winds from adjacent Wolf-Rayet Carbon (WC)
stars. With the DustEM code we determine that the Pistol nebula is composed of
a distribution of very small, transiently-heated grains (10-~35 {\AA}) and that
it exhibits a gradient of decreasing grain size from the south to the north due
to differential sputtering by the winds from the WC stars. Dust in the
G0.120-0.048 nebula is primarily heated by the central star; however, the
nebular gas is ionized externally by the Arches Cluster. Unlike the Pistol
nebula, the G0.120-0.048 nebula is freely expanding into the surrounding
medium. Given independent dust and gas mass estimates we find that the Pistol
and G0.120-0.048 nebulae exhibit similar gas-to-dust mass ratios of ~310 and
~290, respectively. Both nebulae share identical size scales (~ 0.7 pc) which
suggests that they have similar dynamical timescales of ~10^5 yrs, assuming a
shell expansion velocity of v_exp 60 km/s.
