The flowers on these doors are not sitting on a lattice. They are what is left of it.
The whole panel starts as one board. The obvious way to get this effect would be to make a jali screen and glue a carved flower onto it - and you can tell instantly when that has been done, because a glued-on flower has a shadow line all round its base where it meets the lattice, and it sits at a single flat depth rather than growing out of the panel.
So our master Indian artisans work the panel in one piece, and the order matters more than the skill. The floral vine is modelled first, to its full depth, while the board is still solid - because a solid board can be held firmly, and carving needs the work to be still. Only when the flowers are finished is the lattice pierced through the ground around them.
That order cannot be reversed. Pierce the lattice first and the panel becomes a fragile web with nothing to clamp and nothing to resist the tool; every mallet blow after that risks the whole thing.
Solid first, then open. The flowers are older than the holes.