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 μm of the region containing these three LBVs, obtained with SOFIA using FORCAST. We argue that 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. However, no detection of hot dust associated with qF362 is made. 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-1) winds from adjacent Wolf-Rayet Carbon (WC) stars. From fits to the spectral energy distribution (SED) of the Pistol nebula with the DustEM code we determine that the Pistol nebula is composed of a distribution of very small, transiently heated grains (10 to 35 Å) having a total dust mass of 0.03 M⊙, and that it exhibits a gradient of decreasing grain size from south to north due to differential sputtering by the winds from the WC stars. The total IR luminosity of the Pistol nebula is 5.2 × 105L⊙. 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. A grain size distribution identical to that of the non-sputtered region of the Pistol nebula satisfies the constraints placed on the G0.120-0.048 nebula from DustEM model fits to its SED and implies a total dust mass of 0.021 M⊙. The total IR luminosity of the G0.120-0.048 nebula is 105L⊙. From Paschen-α and 6 cm observations we determine a total gas mass of 9.3 M⊙and 6.2 M⊙for the Pistol and G0.120-0.048 nebulae, respectively. Given the 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 and , respectively. Both nebulae share identical size scales (0.7 pc) which suggests that they have similar dynamical timescales of 104yr, assuming a shell expansion velocity of vexp= 60 km s-1. © 2014. The American Astronomical Society. All rights reserved.