TL;DR: If LibreOffice Portable behaves clumsy, try the installer.
Now the long version:
Both current versions of LibreOffice Portable (fresh (24.x) and previous (7.x)) are not responsive. It takes a bit of time until the program executes an input, be it moving the cursor or writing text. One can notice that the cursor does not blink regularly, but it looks like a blinking cursor with severe hiccups. This is a relatively new problem for me (using LibreOffice Portable for years), it's apparently a very rare problem, and it's probably next to impossible to find any solution. As I mentioned, I never had that problem before, and no, there were no groundbreaking changes of hardware, software or configuration.
The portable version of OpenOffice does not show this problem. All is fine and fluent. However, there are some compatibility issues with the books that I have written in LibreOffice.
The installed version of LibreOffice works perfectly and, no surprise here, is fully compatible.
Where is LibreOffice Portable running from? If an external drive, have you tried temporarily installing it to your Desktop directory and seeing if it's ok there? It's fine here.
Sometimes, the impossible can become possible, if you're awesome!