Hi Victoria! Welcome to NGA / ATP.
I don't know lilies, but in my opinion, anything marketed as "sand", even "extra coarse sand", has too much fine sand to improve drainage in potting soil. To "open up" potting soil, something larger than "sand" is needed: like "grit". "Perlite" is a good example of the size needed. Maybe "coarse Perlite" is better for the purpose than "medium Perlite".
Coarse sand gets as big as 1 mm, which is still a little small. I found one system that has a category "very coarse sand", which is the 1 mm to 2mm size. If you really could find a bag of that, without the 50-70% finer sand that's usually in "coarse sand" products, you could use that.
But a better size for improving drainage is up around 0.1 inch, or 2.5 mm. Grit. Or double-screened crushed stone.
Those are all HEAVY, and relatively expensive per cubic foot.
I buy cheap (but clean and dry) pine bark, either "coarse bark mulch" or "fine bark nuggets". Then I screen it down to the size I want, and try to remove as much fine stuff and dust as I can. Then I chop up the coarse stuff, and re-screen that.
Eventually I get a wheelbarrow or so of bark shreds, fibers and chips with smallest dimension around 2 mm and as long as I can get. I play with the amount of fines until the bark - all by itself - has ~almost~ the openness that I want, but a good bit coarser.
Then I mix that bark with commercial potting mix like Pro-Mix, which is close to what I want but too water-retentive and not airy enough. I'll mix them somewhere between 70-30% and 30-70%, depending on how open I want it and how many "fines" my re-screened bark still has.
Short answer: I wouldn't bother looking for "super-extra-coarse sand" and hoping it isn't 80% medium sand.
You might buy "crushed granite #2 chicken grit" from a feed store.
Or a bag of double-screened crushed stone around 2-mm grain sizes, and "not a lot of dust and fines".
Or play with bark to MAKE what you wnat. (Or pay a lot for double-screened ground bark "fines" and hope they are not ALL fines.
Or pay for Perlite.
Hope something in there was a little helpful!
