That depends on how that VST-plugin works. I dont know it, but you should automate the LMMS- corresponding dial for the VST's pitching-dial, then you will get the same effect on the sample as you have with manual turning of the VST's pitching-dial.
Doing that for each note is going to take looooooooooooooong time and will be quite a piece of work.....!
So IF this PITCH Monster-VST changes the pitch of your Sample when you turn the VST's pitching-dial, then you will get that exact change with the automation!
If manual changing does not influence the sample, then it is not possible. So as i started: It depends on what PITCH Monster can do.
Here are the dial-array where you need to automate the corresponder-dial:

Click the wrench-icon
Then something like this opens:

Find and Automate the VST's pitching-dial.
Remember that automation can be recorded