they should be able to just check you in to LAX. As far as splitting up the bags....never tried that one. I think its check all through or none. Just from a security standpoint Im not even sure its legal. If I was a CSA that wasnt an FTer or some savvy web info type traveler I'd find it a bit odd that 1 checked bag is retrieved at LAX while Im supposed to be checking another 1 through on an international flight. On another note you say the connection is just over 3 hours, should there end up being a delay into LAX of any length which makes making the CX flight tight you may end up with not enough time to retrieve bags and recheck them. As I think the minimum time to check in an international bag at LAX is 60 minutes