When you want to start debugging with SEGGER J-Link lite debugger in Kinetis Design Studio 1.1.1 you must set properly several options otherwise the debugger behave incorrectly (it seems that debugger works but the application execution does not work - e.g. functions are not called).
When you create a new Kinetis Design Studio project (with Processor Expert), write you code and build the application you must also create a debug configuration (open the context menu of the project in the Project Exporer and select Debug As / Debug Configurations...).
In the Debug Configuration window create a new debugger connection for GDB SEGGER J-Link Debugging and set the correct values for the derivative of your project (e.g. MKL25Z128 derivative on FRDM-KL25Z target board):
On the Debugger tab set the device name (see the list of Supported device names) (e.g.set value MKL25Z128xxx4 for the MKL25Z128) and uncheck the Allocate console for semihosting and SWO (it is not supported).
On the Startup tab uncheck Enable semihosting and Enable SWO.
Click on Apply to save the settings. the debugger is connection is set properly now and you should be able to debug your application (click on the Debug button).
Note: You can use this option for the OpenSDA connection when the SEGGER firmware is flashed. SEGGER offers a firmware running on the Freescale OpenSDA platform which makes OpenSDA compatible to J-Link Lite (see pages https://www.segger.com/opensda.html). You can find more details about OpenSDA MSD Bootloader in the OpenSDA User’s Guide document, see http://www.freescale.com/files/32bit/doc/user_guide/OPENSDAUG.pdf