"Currently closed"???
...oh right... As in winter closure. If you go, you will find the "road closed" sign that many (or most?) people drive around (and travel at their own risk!). See the picture
here. Inyo County Road Dept installed a locked gate that only lasted one season, because of all the ruckus raised by local businesses -- locked gate = tourists not stopping in Lone Pine! Before the gate installation, the CHP went up once in a blue moon and wrote a few parking tickets. Who knows what they will do after the gate fiasco.
The most recently posted info is that they have one-lane access, with a flagman and pilot car running one-way traffic. They have warned that the road could have long (i.e. several hours) closures on week days, but I don't think that is the case just yet.
...and you will have to head over the Sierra at either Tahoe or via Bakersfield, since all the passes in between are closed. But you knew that.
By the way, permits are available to all until May 1, and after that, they have never reached the daily quota until Memorial Weekend, so there is no hurry yet to get over there to do any hiking.