I would ask cardi directly
a quick lookup returned a site where their standard headlights fit all levels of trim for 2011. These are noted as standard, not custom in any way
from the site, bold emphasis is mine:
"Headlights Halogen (w/o LED DRL) Set Pair 2011-2018 Toyota Sienna Base/ L/ LE/ XLE/ Limited. Will Not Work With Factory HID Option"
The dimensions are identical, the internal functions differ.
As John Barleycorn mentions, plus there is an appearance difference for the SE, they are "darkened" inside for the sport look, though light output is the same. Just for looks, but if you look at an LE and SE side by side, you will see it. I believe 2015+ the LED DRLs come into play, but don't quote me there.
Fitment wise, no change for 2011-2015 across all trims. I think the later modes fit too but the connectors changed from 2015 onwards with the introduction of the LED DRL. Does your limited have HID's? Best option is to take the harness connector pics from your Van and send it to the vendor for confirmation