We present textit{Spitzer Space Telescope} variability monitoring observations of three low-gravity L dwarfs with previous detections of variability in the near-IR, 2MASS J0045+16, 2MASS J0501-00 and 2MASS J1425-36. We detect significant, periodic variability in two of our targets, 2MASS J0045+16 and 2MASS J0501-00. We do not detect variability in 2MASS J1425-36. Combining our new rotation periods with rotational velocities, we calculate inclination angles of $22pm1^{circ}$, ${60^{+13 }_{-8}} ^{circ}$ and $52^{+19}_{-13}~^{circ}$ for 2MASS J0045+16, 2MASS J0501-00 and 2MASS J1425-36 respectively. Our three new objects are consistent with the tentative relations between inclination, amplitude and color anomaly previously reported. Objects with the highest variability amplitudes are inclined equator-on, while the maximum observed amplitude decreases as the inclination angle decreases. We also find a correlation between the inclination angle and $(J-K)_{mathrm{2MASS}}$ color anomaly for the sample of objects with measured inclinations. Compiling the entire sample of brown dwarfs with textit{Spitzer} variability detections, we find no enhancement in amplitude for young, early-L dwarfs compared to the field dwarf population. We find a possible enhancement in amplitude of low-gravity late-L dwarfs at $4.5~mu$m. We do not find a correlation between amplitude ratio and spectral type for field dwarfs or for the young population. Finally, we compile the rotation periods of a large sample of brown dwarfs with ages 1 Myr to 1 Gyr and compare the rotation rates predicted by evolutionary models assuming angular momentum conservation. We find that the rotation rates of the current sample of brown dwarfs fall within the expected range set by evolutionary models and breakup limits.
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