This directly from the data sheet:
LO Inputs. No internal bias; optimally biased by an LVDS driver. For best performance, these inputs should be driven differentially. If driven by a single-ended sine wave at 4LOP or 4LON, the signal level should be >0 dBm (50 Ω) with external bias resistors.
Besides, even if you input a sine wave, it will become a square wave after the internal LO divider. I suggest this again, you should research the Gilbert Cell Mixer.
Thanks for pointing towards right part of data sheet. I actually read this part but as i could not found any mentioning of sine wave frequency range explicitly (as given in AD8333 data sheet), i was confused.
As for as your second point is concerned, it means that if we apply square wave at 4LOP pin or sine wave at this pin, the I/Q outputs will be same. Am i right?