Okay on 20 x 20 tiles?
Do you always use level cure for 20 x 20 tile install? The flooring in question does not look uneven to most of the tile people that came to measure. One woman suggested level cure, two other tile reps said it wasn't necessary from what they saw of my flooring.
I don't know what level cure is. I think you should make sure that you need it first. You haven't supplied any information in your post to allow anyone to help you.
How about dimensions of the room and how off level it is?
I also am not familiar with "level cure" , but have used a product called "LevelQuick" which is a self leveling product to use on uneven floors in prep. for sheet flooring. Ceramic tile can usually deal with irregularites due to the thickness of the mortar. I understand large tiles like yours bring in a whole new dimension of issues. I recommend you check with our friends at the tile forum www.johnbridge.com
They will have an answer for you.
The bigger the tile, the harder it is to get a perfectly flat installation. the objective is to keep all tiles in plane so that there are no lips from one to another. On some tile, this is impossible, since the tiles themselves aren't consistent (have warps, cups, twists to them so even on a flat surface, they won't lay flat). The only way to handle those is with a wide grout joint and let the grout bridge the difference.
Assuming the tile themselves are flat, then there should be no lips between them. Any bump, ridge, etc. the tile sits over can make this much more challenging, and a prefectly level floor makes the job much easier to get a good result. This can be done when setting in the thinset by building it up where needed and thinning it out as well, but takes much more time and skill (and materials in the extra mortar).
Important note - I'm not a pro
Retired Defense Industry Engineer; Schluter 2.5-day Workshop Completed 2013, 2014