There may not be an EPSG code for a specific LAEA, unless some agency has used it (such as a national geological organization, or a petroleum company), and the EPSG (or other authority such as ESRI or OGC), have assigned it a code, and someone has had the need to put it into the database for their application.
The clue is in the
central_meridian parameter, which in your case is -75, and the
Latitude_Of_Origin parameter (which point to a Peru-centred map). A LAEA projection must specify these lines, but they can be anywhere on the globe, so there would have to be infinite number of
authority codes to cover them all!
It must be remembered that EPSG codes aren't "magic", they are only a convenience in looking up the projection parameters in a database (and as a shorthand when talking to colleagues); and it is these parameters that are used to transform the data from one CS/projection to another.
What you could do if you use this projection often, is to assign your own codes in whichever database you use. Proj.4 (which is the de facto library for cartographic projection) allows you to create your own text file databases mapping codes to projection parameters, or even append to an existing one like the file called
epsg in the Proj.4 directory. An example of this is the "Google" Spherical Mercator projection that was originally assigned to EPSG:900913 which is way off the bottom of the official list. Eventually the EPSG adopted it and gave it the official code EPSG:3857