I've always stayed in Redding at one of the Motel 6's when I've needed cheap sleeps. There's one at the south end of town. Takes about 90 minutes to get to Lassen, IIRC.
I just looked at the NPS website - "The crew began plowing the southwest portion of the road on March 31st. They are currently 3.5 miles north of the Southwest parking area, rapidly approaching Emerald Lake. Visitors can drive to the Sulphur Works parking area, 1 mile from the Southwest Entrance. Beyond there, the road is closed to vehicle traffic. If visiting Monday-Thursday you must watch for moving heavy equipment, and use extreme caution. Operators will not hear you approach. Snowshoeing and skiing opportunities are available from either entrance. Complete opening usually happens by mid to late June. This page is not updated on weekends."