Fan switch compatibility
Looking at the specifications, both the Emerson Loft Fan CF765WW and Emerson CF144/CF152 Curva Fan appear to use PSC motors, so they should be compatible with any typical fan speed control, including the Lagrand AAFN4S16AM4.

I notice that both of these fans are premium models that have the speed controls included in the box.  In the case of the Curva, the package includes a wireless remote and receiver.

Obviously you won't be saving any money by using "off-the-shelf" fan switches with these.