  In this paper, we derive regular criteria via pressure or gradient of the
velocity in Lorentz spaces to the 3D Navier-Stokes equations. It is shown that
a Leray-Hopf weak solution is regular on $(0,T]$ provided that either the norm
$\|\Pi\|_{L^{p,\infty}(0,T; L ^{q,\infty}(\mathbb{R}^{3}))} $ with $
{2}/{p}+{3}/{q}=2$ $({3}/{2}<q<\infty)$ or $\|\nabla\Pi\|_{L^{p,\infty}(0,T; L
^{q,\infty}(\mathbb{R}^{3}))} $ with $ {2}/{p}+{3}/{q}=3$ $(1<q<\infty)$ is
small. This gives an affirmative answer to a question proposed by Suzuki in
[26, Remark 2.4, p.3850]. Moreover, regular conditions in terms of $\nabla u$
obtained here generalize known ones to allow the time direction to belong to
Lorentz spaces.
