  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 $22\pm1^{\circ}$, ${60^{+13 }_{-8}} ^{\circ}$ 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.
