Airlines are worse today anout interlining bags than they used to be, but that would seem to be critical here and the worst they could do would be to say no. You definitely don't want to have to claim the bag or go all the way out and then back in, as odds of not hitting a snag in that brief a time aren't good (in MEX they force everyone to go through immigration and customs and then back in, even for connecting flights)

U need an interlined bag and a connections counter on the airside, but I can't say for sure whether LIM has that with that airline represented. I'd try to go the carry-on route if at all possible.