B737-300 flight crew on the RIIVR arrival into LAX had a course deviation. Late runway assignment by ATC; according to the crew; was a contributing factor.

Narrative

Enroute to LAX; ATC cleared us direct GRAMM intersection very early in the flight. GRAMM intersection is on the RIIVR Arrival. The FMC was programmed to GRAMM intersection only. No runway was entered as SoCal Approach normally gives you this when you check in. We were handed off to SoCal Approach right at GRAMM intersection (the end of our route). He assigned us 25L. We programmed 25L in the CDU and selected the RIIVR TRANS. When RUSTT and HABSO did not appear in the arrival sequence; the First Officer entered it manually. By this time we were over RUSTT and LNAV wanted to take us back to the fix. I immediately knew we were going thru the 25 localizer and selected 109.9 and started turning towards the localizer. I think we were about 1 dot south of course. I called SoCal immediately and told them we were off the arrival and asked if there was a problem. He quickly gave us a descent to 12;000 and direct RIIVR. (I believe I am remembering that correctly.) We were pretty busy at this time attempting to correct the problem and making sure we were on our descent profile as well. The remainder of the flight was uneventful and when we landed; LAX Tower asked us to call SoCal Approach on the phone. I called them as soon as we could and discussed the problem; ensuring that there had not been a conflict with other traffic. We discussed this being a problem and I assured him that I was aware of it. By being cleared direct GRAMM and not having any fixes in after this intersection; we should have entered RUSTT and HABSO manually. Then the aircraft would have continued to these fixes as we entered 25L in the CDU with the RIIVR transition.