Air
Los Angeles International Airport: Airport Code (LAX)
Taxi
Yellow Cab Phone: (424) 222-2222
Independent Cab Co. Phone: (310) 659-8294
United Taxi Phone: (800) 822-8294
Bell Cab Phone: (888) 481-2345
Shuttle/Uber Services
Tiverton House is located in Westwood area. For travel from LAX to Westwood, there is a flyaway shuttle service that directly goes from LAX to Westwood
http://www.lawa.org/FlyAway/Default.aspx
Make sure that you get on the bus bound for Westwood. It is $10 one way (only credit card accepted).
There is Uber service at LAX now. You need to go to the departure level at LAX. Then at each terminal, there is a station for shuttle service and Uber driver will pick you up at the station.
Directions
For additional information, see: http://www.ucla.edu/maps-directions-parking/