  In Lyman-alpha forest measurements it is generally assumed that quasars are
mere background light sources which are uncorrelated with the forest.
Gravitational lensing of the quasars violates this assumption. This effect
leads to a measurement bias, but more interestingly it provides a valuable
signal. The lensing signal can be extracted by correlating quasar magnitudes
with the flux power spectrum and with the flux decrement. These correlations
will be challenging to measure but their detection provides a direct measure of
how features in the Lyman-alpha forest trace the underlying mass density field.
Observing them will test the fundamental hypothesis that fluctuations in the
forest are predominantly driven by fluctuations in mass, rather than in the
ionizing background, helium reionization or winds. We discuss ways to
disentangle the lensing signal from other sources of such correlations,
including dust, continuum and background residuals. The lensing-induced
measurement bias arises from sample selection: one preferentially collects
spectra of magnified quasars which are behind overdense regions. This
measurement bias is ~0.1-1% for the flux power spectrum, optical depth and the
flux probability distribution. Since the effect is systematic, quantities such
as the amplitude of the flux power spectrum averaged across scales should be
interpreted with care.
