Does LAX offer shuttle services to Amtrak? If not what cabs services are there?
LAX itself doesn't offer a shuttle, however, there are third party companies that will get you there. Prime Time Shuttle, for example, does rides to and from LAX to Union Station.
Fly Away is another option, probably the cheapest and the one that I would take. You will see signs for this around baggage claim, follow the signs and hop on the Fly Away buses. This will take you directly there, I believe it's the last stop.
The most expensive method would be to get a cab and have them take you there.
While I am not as familiar, you can also take the Metro. For this you will have to take a shuttle from LAX to the Metro Station and then the Metro to Union Station.
Allocate a little over an hour for this journey, the drive itself takes 45 minutes without traffic and you need to account for time waiting for the shuttle/bus/taxi to arrive and then walking time.
Best of luck,
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