Is there any way to control the PowerLab with MATLAB or another third party software without using LabChart, LabTutor, or Lt?

No. PowerLab units are fully software controlled by LabChart, Lt, or LabStation and cannot be controlled by third party software. 
However, it is possible to control LabChart for Windows, version 7.3.5 and later, with custom scripting in MATLAB or a custom C++ program, and also stream data into another software package.  For an example of how this can be done in MATLAB, a sample script is located HERE.  It will create a tab called 'MATLAB Sampling' in LabChart's Welcome Center, which contains instructions for how to use the demo.
Additionally, there are more example MATLAB scripts relating to this which are included with every install of LabChart. You can find them in the MATLAB Automation Scripts section of the Getting Started tab in the Welcome Center.