I hate how this question will sound, but just concerned about safety….the mass transit where I live has been really sadly impacted by the opioid epidemic (open drug use at all times of day, violent crimes, etc)…so I’m a bit cautious. Thank you for understanding as we are travelling with our young kids.
Just found this in a search. I took public transportation in LA in July and August and had no serious issues. I had no issues taking my 12 year old on any bus or rail. There were homeless riding and also the occasional weirdness, but that's the case with any public transportation. I didn't see any open drug use and never feared for my safety. We did see some mentally ill people just wandering around Metro subway stations, but they were harmless. We actually took route 460 from Anaheim to LA and got off near the arena (former Staples Center) in order to transfer to a local route to get to Little Tokyo.
LA Metro is really diverse though. Their newest buses are great, with fast Wi-Fi (I think it's connected to 5G) and USB outlets under every seat. The Red/Purple lines are older heavy style subways. We took the Gold line from Santa Monica, and that's modern light rail. There were no shortage of families and just people enjoying a day at the beach.
I certainly wouldn't worry about anything after a Lakers game. There will be tons of people taking public transportation and plenty of law enforcement out, including riding on buses and light rail. Right now a Metro day pass is $3.50 (until the end of 2022), although one will also need a TAP interagency fare card ($2) to load a day pass. The 460 that goes between LA and Anaheim has a one-way cash fare of $2.50, but it's included with a day pass. They supposedly sell those on route 460 buses, but the driver told us they ran out and just let us on. We ended up getting the cards and day passes in LA at a subway station anyways, so no harm, no foul.
The train (MetroLink or Amtrak California's Pacific Surfliner) aren't really all that great because their schedules probably won't work. And you would probably need to take public transportation to get to LA Union Station to do that.
But 460 is really an oddball route. Even OCTA publishes a schedule even though it's not their bus. Your biggest problem might be that the last southbound bus leaves at about 10:30 PM (weekdays or weekends). I looked up the Nov schedule and about the only game that I'd think would work with the 460 bus would be Nov 26, which is a 5 PM start time. 7 PM night games might work though if you don't stick around and make sure to leave early.
https://www.octa.net/ebusbook/RoutePDF/MetroBusSchedules.pdf
https://cdn.beta.metro.net/wp-content/uploads/2022/06/23220646/460_TT_06-26-22.pdf
Other than that, there's always Uber or Lyft. It would be pricey though because of surge pricing. But I would really consider taking Metro. It's really not that bad, although I'd make sure to get there early, even if it means leaving before the game is over.
If you're willing to make a full day, you might consider staying overnight. The hotels in the area are some of the best in LA.
