The Kerr effect is a second order electroptical effect that refracts light
Second order because bending is proportional to the square of the electric field strength rather than the Pockels effect where bending is proportional to the electric field strength.
Ionization causes an electric field although mirages are produced by local atmospheric heating effects. At a high enough light intensity ionization becomes probable, hence the idea of a "laser lightning rod" to improve the chances of safe rocket launches when thunder clouds were nearby.
Didn't everyone know this?
Given I've never seen a laser lightning rod system ever fielded I've got serious doubts about something that does something this tricky (from, if you believe the video, a multi Mach aircraft while in flight).