Plenty of fares are filed at lower prices, ranging from NLX0B6C0 at GBP 521 (with restrictions) to a fully flex YNN0Y6C5 at GBP2573. Looking for example at 20 Oct and 23 Oct, availability in both flights is:
LOS-LHR F9 A8 J9 C9 D9 R9 I9 W9 E9 T8 Y9 B9 H9 K9 M9 L9 V9 S9 N9 Q9 O9
LHR-LOS F9 A9 J9 C9 D9 R9 I9 W9 E9 T9 Y9 B9 H9 K9 M9 L9 V9 S9 N9 Q9 O9
but for some reason BA is only offering Y booking class, rather than any lower booking class.
Expedia offers a fare NLN0B6C0 in N booking class for GBP947 total.
I suspect BA's IT is faulty again and they are not offering all the fare classes available.
If you want to book, you could phone BA and see if the more reasonable fares are available; if they are, ask for a waiver of the phone booking fee because the BA website is malfunctioning.