The below link is for the Fly A Way service that runs to Union Station, a short distance from the hotel.
Fare: $8.00 one way
http://www.lawa.org/welcome_lax.aspx?id=4696

The Omni at California Plaza operates a complimentary town car service. At Union Station you can contact the hotel directly and ask for the town car service to pick you up. However, it is on a first come first serve basis and it runs
7 a.m. – 10 p.m. daily

Taxi:

Set charge from LAX to hotel approximately $53

Private Car Service /Shuttle:

TLA Limousine - Los Angeles
Toll Free: 800-589-6185
Email:   reservations@tlalimo.com
Website: www.tlalimo.com


Additional options can be found by visiting:
http://www.lawa.org/welcomeLAX.aspx