You'll need to do some basic design work to figure out how much lumber you'll need.
If you'll be doing a modern-style yurt, you have the crown ring, maybe 40 roof poles (often machine rated 2x4 or 2x6), vertical supports at the wall end under each rafter, plus a light-weight lattice. So you'd need to know the crown ring diameter, roof pitch, and wall height to estimate total lumber. Since the lattice will only be giving shape/supporting the wall canvas, it can be pretty lightweight--say 1/8" thick strips setup on 12-16" spacing. You could potentially rip the lathe from high quality lumber (knots will problematic).
If you're leaning towards a more tradition-style yurt, for the larger yurts think upwards of 90 roof poles (2x2) each supported by a junction on top of your lattice. The lattice should also be a lot thicker, like 1/2" or so. Lattice junction/roof pole spacing at the wall would be around 10-12". You'll need a little more than twice as many lathe pieces as roof poles. Crown ring supports are also recommended, especially for snow or high wind areas.
Like Bob mentioned, some engineering is going to be important with the larger yurts. I think it is important to be aware of the forces & the risks. A pretty low, basic snow loading in a lot of areas is ~20 lbs/sq ft. A 28 ft yurt would need to support up to 12300 lbs (5.5 metric tons) in that case. There's also wind loads to consider (especially if near open waters), the weight of the canvas & insulation
(pretty minor), and on the special occasion getting up onto the yurt roof. If you can run the numbers and feel comfortable with doing it yourself, then by all means do so--that is your choice. Or if you have yurt cultural experience that informs your design (ie, trial & error over centuries...).
An excellent site, with online calculators, is https://simplydifferently.org/Yurt_Diary