  Gravitational lensing is a potentially powerful tool for elucidating the
origin of gamma-ray emission from distant sources. Cosmic lenses magnify the
emission from distance sources and produce time delays between mirage images.
Gravitationally-induced time delays depend on the position of the emitting
regions in the source plane. The Fermi/LAT satellite continuously monitors the
entire sky and detects gamma-ray flares, including those from
gravitationally-lensed blazars. Therefore, temporal resolution at gamma-ray
energies can be used to measure these time delays, which, in turn, can be used
to resolve the origin of the gamma-ray flares spatially. We provide a guide to
the application and Monte Carlo simulation of three techniques for analyzing
these unresolved light curves: the Autocorrelation Function, the Double Power
Spectrum, and the Maximum Peak Method. We apply these methods to derive time
delays from the gamma-ray light curve of the gravitationally-lensed blazar PKS
1830-211. The result of temporal analysis combined with the properties of the
lens from radio observations yield an improvement in spatial resolution at
gamma-ray energies by a factor of 10000. We analyze four active periods. For
two of these periods, the emission is consistent with origination from the core
and for the other two, the data suggest that the emission region is displaced
from the core by more that ~1.5 kpc. For the core emission, the gamma-ray time
delays, $23\pm0.5$ days and $19.7\pm1.2$ days, are consistent with the radio
time delay $26^{+4}_{-5}$ days.
