While the Pacific Surfliner coach is unreserved, Business Class (there is no "1st Class" on anything except the Acela) is reserved for a specific train. You should be reticketed. Amtrak often does this automatically when their system shows that a connection will be missed.
I think the folks at the Metropolitan Lounge should be able to help you if your connection isn't made.
If there are no Business Class seats on the next train, you will likely be accomodated in coach and the fare difference refunded.
I am with Ryan, there are numerous Pacific Surfliners (9 a day now,I think) and which train you are ticketed on would help. Also, AmtrakDelays.com would give you a more accurate picture of the trains on time performance into LA than the simple percentage on Amtrak's website, as it will give the actual delays.