Hi Nicolas!
For Mexico, INEGI makes 5m DEMs and DSMs derived from LiDAR at:
http://www.inegi.org.mx/geo/contenidos/datosrelieve/continental/presentacion.aspx with coverage for most of the country. While this most likely is not ideal for your intents, it might be a starting point to verify coverage for your AOI. You may then try your luck at obtaining the LAS/LAZ files from INEGI through directly liaising with them or through a "request of access to information" (hopefully you speak/write good Spanish).
Additionally, a few years ago there was a big announcement of Raw LiDAR released for big areas in Campeche and Chiapas under the auspicies of the REDD+ Alliance. The links were served out of the Alliance's portal:
https://www.tncmx.org/alianza-mredd/ but are no longer to be found. You may contact TNC or the Rainforest Alliance who led the work as that data must still be public.
I believe these are your only possible avenues (if that).
I'm McGill alumni (NEO student), and happy to help.
Good luck!