Unless you fly in on the weekend, Metrolink should be available at BUR, which takes you to LA Union Station in downtown. From there, I am not sure how to get to the subways, though.
LAX
Thank you!
For some reason I assumed all my options were listed on the "Bus and Rail System Map" from metro.net and the associated trip planning tool...
I saw people mention Metrolink on this board, but assumed it had something to do with the Metro Rail in the Metro network...
The subway line one block from my hotel does indeed run to Union Station so this appears to be the best option.