I doubt you can check your bags through to BUE and they are all domestic flights so it isnt as if you need to clear customs along the way.
Most LAN flights include a "free" stopover, even on the cheapest tickets, but the "free-ness" of such a stopover are somewhat of a misnomer as you also have to pay the change fee and the recalculation of the following segment if applicable.
If LAN are offering to change your destination to BUE for the change fee without any additional penalties then that is probably your most economical option