Air Traffic Controller reported misidentifying an aircraft as VFR when they were IFR resulting in the aircraft flying towards terrain. The controller issued a low altitude alert and the pilot landed safely at the airport.

Narrative

Aircraft X was on a vector from the Lake sector for a visual approach to HND. I have no idea why but in my mind I knew the aircraft was on a VFR flight plan which was incorrect. I issued a 270 heading and altitude their discretion when they were in a position where I would have let them start down for the airport. The pilot did not question the lack of altitude assignment for an IFR flight and started a gradual descent. HND tower called for a release and said they would provide visual separation with the arrival. That was when I realized that I essentially issued a VFR descent clearance to an IFR aircraft. Aircraft X was in a position where it was reasonable to expect them to see the airport so I pointed it out. They responded with 'looking' I then issued a low altitude alert and a climb as the aircraft was at 6000 in a 6300 MVA. The pilot reported the airport in sight and was then issued a visual approach clearance.A major contributing factor to this is exhaustion. I am on the non preferred overtime list and just in the last 5 weeks I have been forced to work 56 hours of overtime. We are now 5 weeks into this government shutdown we are taking more sick leave hits than ever so every single shift is extremely short. This is not a mistake I would normally make I have never done this before. Even when we are not in a shutdown the L30 staffing is somewhere around 50% I have been on the non preferred OT list all year and I still have something around 300 hours of OT. This place is killing all of us and our new manager is giving out sick leave letters as well as monitoring and mandating when the OS (Operations Supervisor) relives a controller off of position at the end of our shifts. I don't want to sound like I am blowing things out of proportion. But; I can not express clearly enough how bad it currently is at L30 I have been here a long time and have never seen this before. I made a mistake and I take full responsibility for it. The current culture here is going to cause a huge problem. I am in the middle of several family emergencies all while dealing with not getting paid. There is no possible way to take time off to process anything. It is simply unacceptable the way we are being treated; everyone is exhausted.