  Gravitational lensing time delays offer an avenue to measure the Hubble
parameter $H_0$, with some analyses suggesting a tension with early-type probes
of $H_0$. The lensing measurements must mitigate systematic uncertainties due
to the mass modelling of lens galaxies. In particular, a core component in the
lens density profile would form an approximate local mass sheet degeneracy and
could bias $H_0$ in the right direction to solve the lensing tension. We
consider ultralight dark matter as a possible mechanism to generate such
galactic cores. We show that cores of roughly the required properties could
arise naturally if an ultralight axion of mass $m\sim10^{-25}$ eV makes up a
fraction of order ten percent of the total cosmological dark matter density. A
relic abundance of this order of magnitude could come from vacuum misalignment.
Stellar kinematics measurements of well-resolved massive galaxies (including
the Milky Way) may offer a way to test the scenario. Kinematics analyses aiming
to test the core hypothesis in massive elliptical lens galaxies should not, in
general, adopt the perfect mass sheet limit, as ignoring the finite extent of
an actual physical core could lead to significant systematic errors.
