The 'Add XY Coordinates' tool is generally meant for adding coordinate fields to data tables already in arcmap. If you've already converted your .LAS to a .SHP then you should be able to add that to your data frame as-is without any special import procedure. It will already have a SHAPE column which has the XY info in it. If you want to expose the X & Y coordinates explicitly in your table (ie, add new columns) then this is the tool for you. Alternatively there is the 'Add XY Data' tool which does more what you're thinking; that is, add data from an existing table into a new layer by telling ArcMap which are the X & Y fields. However, it sounds like you've already done the conversion and are just looking to expose the XY data in ArcMap.
I can't speak to working with .LAS in ArcMap specifically but did dig up a few links for you:
http://desktop.arcgis.com/en/arcmap/10.3/manage-data/las-dataset/what-is-a-las-dataset-.htm
