Where you live and work and play really makes a difference, if you want to move to LA without a car do some research.
Where are the jobs you need located (remember they will probably be in pockets, tech for one example is in Hollywood near the Boulevard, Pasadena, Glendale, DTLA, Culver City, Santa Monica).
The bus system is usable if required but still quite awful and slow especially if you have to transfer, but Metro Transit's rail is quite robust and can work if you live and work on a line like i do. Everything connects to DTLA, but SM to DTLA is 1hr+.
I recommend short term rentals to check out a neighborhood - airbnb for example is cheaper if you stay at longer intervals. Days > Week > Month. I stayed in hollywood for a month at an airbnb (it felt very similar to a hostel), before i settled on a neighborhood. Some neighborhoods are much more affordable, try Zumper to get an idea of prices to understand what's even possible for you (DTLA for example is not cheap if you don't have a roommate, and will certainly price a lot of individuals out, but NoHo and Hollywood are still more affordable).
The scariest thing about LA is if there aren't a lot of jobs in your industry that you're interested in or fit your needs, the idea of trying to find a new job paralyzes you to the neigborhood you live in or near. Tech is one industry example of this.
One of the great things about LA is exploring the larger city, so not having a car will make that difficult, and there's a lot of great places that benefit from a car (Santa Barbara, Palm Springs, Vegas, Inland Empire, San Diego, etc).
I would be worried if you have specific needs, as finding specialized doctors might be difficult since sometimes who you need to see is in Toluca Lake, Brentwood, West Hollywood, etc.
I drive maybe once every week or two, but live in Little Tokyo off the red line, and commute to hollywood off the redline. It works great, but i do feel trapped should i ever need to change jobs.