Yeah, that's pretty bad....

Going to need to bring hiking gear when we go so HBO is definitely not an option. Thanks to your feedback will avoid same day connection even though the HAM-MAD doesn't leave until late night. Will try 24+ hrs advance to give a buffer... or alternatively travel there with OW. BA might be a bit more keen to send the luggage to LIM if you are showing them you have a further OW connection. (Even though technically it's only half OW...)

In the meantime happy holidays and hope you manage to make the most of your clothing expenses from both LX and LA!