In this paper, we show that the predual spaces of some Lorentz sequence spaces are strictly convex renormable such that any point of the unit sphere is not an extreme point of the unit ball of the dibual. This will partially answer the Question 2. in the paper of Peter Morris.
"DISAPPEARANCE OF EXTREME POINTS: $d_*(w,1)$ CASE." Taiwanese J. Math. 14 (4) 1457 - 1463, 2010. https://doi.org/10.11650/twjm/1500405960