None as of October 2020. Previous fire damage visible, but no road closure.
Need to Know
Beware that the other trail listed as Lexington Arch Trail is not a trail - it is a hike/scramble up the wash below the arch.
The Arch is in Great Basin National Park, but the access road and trail are not.
As of October 2020, the road is quite passable to most vehicles with standard clearance. My Subaru Crosstrek had no issues. Of note, if you are coming from Great Basin National Park, don't follow your map program's route, as the road is more difficult. Instead, keep going along the highway until you see the sign for Lexington Arch. The road is passable.
The trailhead itself isn't marked. The road ends in a wash with a small turnaround amongst burned trees and the occasional free-range cattle. Park where you can, then follow the wash. There are periodic signs and ducks marking the trail. The trail will cross the wash a few times before it splits off to the left (south) and ascends the hill in a series of switchbacks. The uploaded route ends at a nice bench with a great view of the arch. There is a trail that extends beyond this, but I didn't find the views much better. Return the way you came.