This looks OK:
lines3d(x=0,y = 0:range(X)[2], z=0, col="red", size=3)
lines3d(x=range(Z)[1]:range(Z)[2], y=0, z=0, col="red", size=3)
lines3d(x=0,y=0, z=range(Y)[1]:range(Y)[2], col="red", size=3)
But this looks better(IMO):
lines3d(x=0,y = 0:range(X)[2], z=0, col="red", size=3)
lines3d(x=0:range(Z)[2], y=0, z=0, col="red", size=3)
lines3d(x=0,y=0, z=0:range(Y)[2], col="red", size=3)
Maybe change the color of the axes to 'blue'?