If you're looking to get your data into an access database you could skip the middle conversion step entirely (or rather have ArcGIS handle it for you) by transferring your data to a personal geodatabase, which in reality is an access database.
From ArcGIS you can use the Create Personal Geodatabase tool to create the access database, and then you should be able to just copy your data across (though I'd export a table to geodatabase and copy the table so you don't waste memory and copy geometries if you don't need them).
Alternately (depending on your version of access) if you already have a database (as .mdb) you don't need to create files to copy them across.
Alternately if you're comfortable with command line utilities OGR supports FileGDB and various other formats including CSV, so you can dump your data out of your geodatabase using ogr2ogr.
A shapefile (.shp) is a vector data storage format for storing the location, shape, and attributes of geographic features. A shapefile is stored in a set of related files and contains one feature class.
A layer file (.lyr) is a file that stores the path to a source dataset and other layer properties, including symbology.
In comparison to a shapefile, a layer file is a just a link\reference to actual data, such as a shapefile, feature class, etc. It is not actual data because it does not store the data's attributes or geometry. A layer file primarily stores the symbology for a feature and other layer properties related to what is seen when the data is viewed in a GIS application.
For example, if a layer file is sent to a user on another machine without the data it was created from, it does not display on the map because it does not contain the source data. To get the data to display properly, the user must have the layer file and the shapefile it references.
This is where utilizing layer packages eases the processing of migrating data, because layer packages store both the layer file and source data. For more information about layer packages, see the Web help topic. (http://support.esri.com/es/knowledgebase/techarticles/detail/40057)
Basically your layer is already a shapefile.
Best Answer
This could easily be converted into a toolbox script or run directly from the python window in Arcmap. It can be improved by validating the layer name before copying, duplicate naming conventions, drilling into group layers, using different data frames, etc.
But this should get you started for a simple TOC: