I have a 1:05 pm flight on LAN to JFK on a Saturday in January (far in advance but I was able to get business class seats using miles). I will be flying back to LIM from CUZ that same departure day. Is getting a flight that is scheduled to get into LIM at 10:30 am a safe margin on time?? If I fly LAN from CUZ into LIM will they safely check my bags through to JFK?

thanks