Los Angeles International Airport: airport code (LAX)
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
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
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.
For additional information, see: http://www.ucla.edu/maps-directions-parking/