From Apollo/Galileo -

LA3PN9 109.00 218.00 UA ROUTE:0035
VALID SINGLE CONNECT CITIES FROM: WAS TO SFO
ABE ALB ATL AUS BDL BIL BOI BUF BUR CAK CHI CID
CLE CLT CMH COS CRW DAY DEN DFW DSM DTT EUG EWR
FAT GEG GSO HAR HFD HOU ICT IND LAS LAX LNK MIA
MKC MKE MLI MSN MSP MSY NYC OAK OKC OMA ONT ORF
ORL PDX PHF PHL PHX PIT RDU RIC RNO ROA ROC SAN
SAT SBA SEA SJC SLC SMF SNA STL SYR TPA TUL TUS

ADDITIONAL RESTRICTIONS ON ROUTING:
NONE

As you can see, LAX is a valid connection point. Since there are no additional restirctions on routing (e.g., not valid on nonstop flights), you should not have a problem. In fact I just priced a nonstop flight IAD SFO booked in L class and it gave this same LA3PN9 fare and fare basis.