The lithium doublet at 6708{AA} provides an age diagnostic for main sequence FGK dwarfs. We measured the abundance of lithium in 1305 stars with detected transiting planets from the Kepler mission using high-resolution spectroscopy. Our catalog of lithium measurements from this sample has a range of abundance from A(Li)=3.11+/-0.07 to an upper limit of -0.84dex. For a magnitude-limited sample that comprises 960 of the 1305 stars, our Keck-HIRES spectra have a median signal-to-noise ratio of 45 per pixel at ~6700{AA} with spectral resolution {lambda}/{Delta}{lambda}=R=55000. We identify 80 young stars that have A(Li) values greater than the Hyades at their respective effective temperatures; these stars are younger than ~650Myr, the approximate age of the Hyades. We then compare the distribution of A(Li) with planet size, multiplicity, orbital period, and insolation flux. We find larger planets preferentially in younger systems, with an A-D two-sided test p-value=0.002, a>3{sigma} confidence that the older and younger planet samples do not come from the same parent distribution. This is consistent with planet inflation/photoevaporation at early ages. The other planet parameters (Kepler planet multiplicity, orbital period, and insolation flux) are uncorrelated with age.