  Approximately $0.2 \pm 0.2$ of white dwarfs (WDs) show signs of pollution by
metals, which is likely due to the accretion of tidally disrupted planetary
material. Models invoking planet-planet interactions after WD formation
generally cannot explain pollution at cooling times of several Gyr. We consider
a scenario in which a planet is perturbed by Lidov-Kozai oscillations induced
by a binary companion and exacerbated by stellar mass loss, explaining
pollution at long cooling times. Our computed accretion rates are consistent
with observations assuming planetary masses between $\sim 0.01$ and
$1\,M_\mathrm{Mars}$, although nongravitational effects may already be
important for masses $\lesssim 0.3 \, M_\mathrm{Mars}$. The fraction of
polluted WDs in our simulations, $\sim 0.05$, is consistent with observations
of WDs with intermediate cooling times between $\sim 0.1$ and 1 Gyr. For
cooling times $\lesssim 0.1$ Gyr and $\gtrsim 1$ Gyr, our scenario cannot
explain the high observed pollution fractions of up to 0.7. Nevertheless, our
results motivate searches for companions around polluted WDs.
