I second @Michal Mackiewicz's answer (about Fusion/LTK), so I hope this example helps you getting through it.

This is the `PolyCLipData` syntax command (see the manual's page 110):

    PolyClipData [switches] PolyFile OutputFile DataFile

Use an text editor to write the command before running it (such as NotePad++).
Save the file with extension `.bat` (batch file). Don't forget to save the file before running it.

Assume you have:

1. Fusion/LTK under the C: drive.
2. the shapefile file (shapefile.shp) under C:\shapefile
3. the las dataset (lasdata.las) under C:\las

write the following:

    c:\fusion\polyclipdata c:\shapefile\shapefile.shp c:\las\clipped_data.las c:\las\lasdata.las

use the switch `multifile` if you want the las files generated from polygons to be stored in separate files. For example:

    c:\fusion\polyclipdata /multifile c:\shapefile\shapefile.shp c:\las\clipped_data.las c:\las\lasdata.las 

use the `shape` switch together with `multifile` to name your multiple OutputFiles with values embedded in one of PolyFile's dbf column. For example if you want to name the files with the ID information (suppose ID is in the shapefile's first column). Write:

    c:\fusion\polyclipdata /multifile /shape:1,* c:\shapefile\shapefile.shp c:\las\clipped_data.las c:\las\lasdata.las 

-------------------------------  
<sub>For clipping las files using `PolyClipData` with multiple single part shapefiles see the following post:</sub>  
<sub>http://gis.stackexchange.com/questions/150294/clipping-las-data-with-multiple-shapefiles/150502#150502</sub>

<sub>For clipping multiple las files having them embedded in a .txt file as the datafile parameter for `PolyClipData`, refer to the following post:</sub>  
<sub>http://gis.stackexchange.com/questions/154561/clip-multiple-las-files-data-to-polygon-shapefile-using-fusion</sub>

<sub>For clipping multiple las files with shapefiles using [tag:LAStools] (with the `LAStools Production` toolbox) refer to the following post:</sub>  
<sub>http://gis.stackexchange.com/questions/122496/clipping-from-a-tiled-las-dataset-with-lastools-for-arcgis/154989#154989</sub>