Im a solo female international traveler and Ive been using LAX for over 10 years. Ive never felt unsafe or had any issues. Its a very busy place, lots of hustle and bustle and everyone on the arrivals level is either a passenger trying to figure out transport, airport staff or shuttle buses picking up.
I would advice looking at a car service pick up at LAX which will meet you at arrivals.
Uber and Lyft are not allowed to pick up at arrivals any more. LAX has moved all taxi, Uber and Lyft pickups to an area called LAXIT which you would need to get a free shuttle to.