Strong gravitational lensing is an effect whereby massive objects, such as galaxies, can bend light from more distant background sources resulting in multiple images of the same source. Strongly lensed quasars can be used to study the Hubble constant, which measures the expansion rate of the universe, and the lens mass by measuring time delay and image separation. These objects can require years of data to confirm however, so using data from preexisting surveys could greatly reduce the amount of time required to study them. We attempt to use Palomar Transient Factory and Sloan Digital Sky Survey data to detect variability in strongly lensed quasars and to measure time delays, the difference in the amount of time required for light from each quasar image to reach us. We test our procedure using known gravitationally lensed quasars with measured time delays. Results indicate that the coverage of known lensed quasars, as well as the spatial resolution of the Palomar Transient Factory survey telescope combined with the relatively small image separation, may not be sufficient to accurately measure the time delay. Upon our failure to measure the time delays, we run simulations to better understand the angular separation requirements for accurately recovering a time delay from Palomar Transient Factory quality data.