I emailed the Yakama WDFW office last week and was told the only road still closed in the LT was the Murray Road between Hutchins Road and the North Fork.
This is from the Cle Elum Ranger District site:
ROADS: Manastash Road No. 3100, Taneum Road No. 3300 and Peoh Point Road No. 3350 which were damaged by flooding in mid-May remain closed. Many other roads across the district were damaged by the flooding. Engineers are assessing damage and we hope that Taneum Road No. 3300 can be opened to public travel within the coming weeks. There is no estimate on when repairs can be made to roads damaged or destroyed by the recent flood event.