But wait...
Where are they actually going with Axel's plane?
They will go to Canada which is a request from Jill herself, there are even some places where Jill specifically asked Axel without Lucifer's knowledge, of course, and that's why he brought Ann because Ann was helping to take care of everything.
Why not tell her boyfriend of her wish?
Because according to Jill, Lucifer will not understand it, and in the end, Axel will do it.
Jill seemed to have understood Lucifer's own way of thinking. As long as Axel can do it well, why should he intervene!
It was as if that saying stuck to Lucifer according to Jill's point of view on her lover who had not been able to fully adapt to the human world.