A few approaches come to mind on how to accomplish sending a signal from java to trigger a DAQmx device:
1) Create an executable of your Labview code. Use a system call from your java code (assuming it's an not an applet) to launch the executable (trivial). This is the simplest, but is limited by your task (passing data, etc.).
2) Wrap your java code using the JNI interface. Have your Labview code make a call to your java application and check if the task should trigger (CIN node? dll, or similar). If you like puzzles, this is a fun one to try. If you are comfortable using java and C/C++, this would work.
3) If you are deploying this to a desktop, does the computer have multiple serial ports, parallel ports, or USB ports? If yes, perhaps you can use the javax.comm package and loop two ports together. Setup your Labview code to listen for a specific message and then trigger the event. If this works, it would be trivial to pass data back and forth between java and Labview. This is by no means an elegant solution, but it will work reliably and is fairly trivial. I've used the javax.comm package with 115200 baud with good success.
Without more specific data on your particular application, these are all the suggestions I have.
Cheers
JMA