I could not find the refresh rate.
The dogxl240 has a 8MHz SPI interface. There are 240*128=30720 pixel available, so as a max refresh rate there could be 260 frames per second (FPS). Of course there is some overhead and some other timing aspects have to be considered, so it might be lesser than this.
However, the real limitation for the refresh rate will come from the selected interface and the microcontroller (Arduino Board).
I have just tested U8g2 Software emulated SPI (which is known to be very slow) on an Arduino Due in U8g2 full frame mode and received about 2 FPS. I assume with hardware SPI (also supported by U8g2) it will be around 20-30 FPS.
For an Arduino Uno with hardware SPI and u8g2 page mode, you probably should get around 5 FPS.
As a conclusion, I guess, that all Arduino boards should be able to refresh within 200 ms under the assumption, that you use hardware SPI.
If not, there still are some tricks to make it faster with u8g2... just contact me for this.
The other that you suggest, looks like it's not reflective (at least because it seems to have a backlight) and maybe is not readable with direct sunlight:
Yes, it is not reflective, but still it is readable (but of course not as good as reflective). I mean, there is always a tradeoff. It aliexpress display is cheaper and has a backlight (so it is readable in the dark also).
It also depends on your intended usage.
For example I just did the FPS tests with a transflective version of the DOGXL240 in my lab with not so bright artificial light. But I also did not turn on the backlight of the DOGXL240: It is readable, but definitly not as good as a reflective version under the same light conditions.
EVE2 NHD 3.5" 320x240, SPI, FT813 chip driver
Of course this is an option, but still a TFT display is not as good readable as a black/white reflective LCD under bright sunshine.