Storing for 3 weeks, then checking in additional luggage on Mexico airport

My wife travels with a suitcase and a backpack on a return flight AMS-MEX-AMS (operated by KLM).
I travel a roundtrip AMS-SFO-MEX-AMS (operated by KLM/Delta) with just a backpack.

We meet in Mexico City. From there we will have a 3-week vacation in Peru, we together fly a return trip MEX-LIM-MEX (operated by Avianca).
During those 3 weeks she wants to leave the suitcase in Mexico, preferably at the airport.

So:

My wife will arrive at MEX with the suitcase and backpack, leave the airport.
A few days later she comes back to the airport with both, will want to take the backpack on to LIM but leave the suitcase behind.
When arriving back from LIM to MEX (3 weeks later), she wants to pick up the suitcase and make sure that it is also put on the MEX-AMS flight.

Is this possible? Is there luggage storage in Mexico airport in the transfer zone, so that we can pick up that second suitcase when we transfer from our LIM-MEX flight to our MEX-AMS flight (we have approximately 4 hours transfer time)?
If not, what would be good alternatives? Is there storage outside the transfer area? Can she leave the area and 'check back in' with the suitcase? Or can she maybe arrange for a reliable local contact to bring the suitcase to the airport where she picks it up?

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Storing for 3 weeks, then checking in additional luggage on Mexico airport - Young ethnic man in earbuds listening to music while waiting for transport at contemporary subway station

Storing for 3 weeks, then checking in additional luggage on Mexico airport - Worried young businesswoman with suitcase hurrying on flight on urban background

Storing for 3 weeks, then checking in additional luggage on Mexico airport - Positive young businesswoman with suitcase hurrying on flight on urban background

Can airports hold your luggage?

If you have an extremely long layover, you might want to ditch the airport and go explore the city, but dragging luggage along with you can make for a cumbersome exploration. Luckily, most airports have a left luggage service where for a fee bags can be stored at the airport and retrieved before a flight.

How long can you keep an airport locker?

Note that bag storage is only for 48 hours or less. Lockers are emptied after 48 hours.

Can I leave my luggage in Mexico City airport?

Luggage storage facilities operate 24 hours a day, 365 days a year. Rates: MX$150 per locker. They are located at: Terminal 1, by Gates 1 and 8, T1 Gate 1 Tel: (55) 2598 16 60. T1 between Gate 7 and 8.

How early can you check luggage?

For flights within the U.S., as well as most international flights, baggage will generally not be accepted for check-in more than four hours before a scheduled flight departure, although this policy varies by airport and daily check-in counter hours.

Sources: Stack Exchange - This article follows the attribution requirements of Stack Exchange and is licensed under CC BY-SA 3.0.

Images: Artem Beliaikin, Andrea Piacquadio, Gustavo Fring, Gustavo Fring