Hello,
the QGIS toolbox for 2.14.1 (Essen) just received a major update.
It may (!) now work better with the Model Builder in Processing. However, I have not yet done serious work with Processing Models in QGIS yet. For the time being I have only combined LAStools into longer processing workflows by Python scripting them together as you can see with several examples in the "LAStools Pipelines" toolbox.
For the time being you will have to manually update your QGIS toolbox in 2.14.1 (Essen) to the new version as described in the README.txt that you find in the QGIS_toolbox folder of the latest LAStools version (160606) from yesterday.
Regards,
Martin @rapidlasso