We investigate the role of environment on radio galaxy properties by constructing a sample of large ($\gtrsim~100$ kpc), nearby ($z<0.3$) radio sources identified as part of the Radio Galaxy Zoo citizen science project. Our sample consists of 16 Fanaroff-Riley Type II (FR-II) sources, 6 FR-I sources, and 1 source with a hybrid morphology. FR-I sources appear to be hosted by more massive galaxies, consistent with previous studies. In the FR-II sample, we compare the degree of asymmetry in radio lobe properties to asymmetry in the radio source environment, quantified through optical galaxy clustering. We find that the length of radio lobes in FR-II sources is anticorrelated with both galaxy clustering and lobe luminosity. These results are in quantitative agreement with predictions from radio source dynamical models and suggest that galaxy clustering provides a useful proxy for the ambient gas density distribution encountered by the radio lobes.