  We prove a general lower bound on Christoffel function on planar convex
domains in terms of a modification of the parallel section function of the
domain. For a certain class of planar convex domains, in combination with a
recent general upper bound, this allows to compute the pointwise behavior of
Christoffel function. We illustrate this approach for the domains
$\{(x,y):|x|^\alpha+|y|^\alpha\le1\}$, $1<\alpha<2$, and compute up to a
constant factor the required modification of the parallel section function,
and, consequently, Christoffel function at an arbitrary interior point of the
domain.
