Add the cashews and oats to a food processor and process until crumbled up into small pieces.
Add the pitted dates, walnuts and coconut oil to the food processor and process until the mixture can stick together between your fingers. If it needs to be more sticky you can add some more coconut oil.
Press the mixture into the bottom and sides of a tart pan and compress it down. Use a flat bottomed glass to press the base down and make it smooth. Set the base aside.
To make the filling:
Add all of the ingredients for the filling into a high-speed blender. Blend until the filling is completely smooth.
Pour the filling over the base in the prepared tart pan. Tap the tart pan lightly against the counter to remove any bubbles. Cover and refrigerate for 4 hours or overnight.
Once the vegan key lime pie has set, remove from the refrigerator, slice and serve.
Store in the refrigerator, covered, for up to 5 days.