I don't like the cut of the crossfader. Can I adjust it?

Yes.

You can adjust crossfader curve in Serato DJ Lite [Setup]> [Mixer] tab.
For details, refer to the Instruction Manual > "Serato DJ Lite" > "Setting the crossfader curve".
For adjusting crossfader cut lag, see "Changing the settings" > "Utilities mode settings".
You can read the Instruction Manual [here].

• Crossfader curve affects the way the sound changes when you slide the crossfader. You can adjust it to suit your preference when scratching or mixing. Cut lag is the length of the silent zone at both ends of the crossfader.