By looking at your specifications it is probably due to your low specs and computer age. When play games such as LoL when running around normally you will be using less CPU and GPU usage, but as soon as you enter into combat then more "power" is required from the CPU and GPU. As your pc is fairly old it wont be using the best of its performance as you will lose some over time, for example a car will lose horse power over time.
Personally the best way to get better performance would be to upgrade but if you haven't got the money for that then you can try these:
1) clean your pc of any cookies, unwanted data and do a general sweep with your antivirus software.
2) you can open up the game using less RAM by right clicking the game .exe, creating a shortcut. Then right click the shortcut and go to "Properties", "Web Document" and in "URL" at the end place ("-force-opengl"). This will open the game using opengl and not Direct3D and can save your around 1GB of Ram.
:http://forum.kerbalspaceprogram.com/index.php?/topic/76031-less-memory-usage-by-using-opengl/ Ksp is an example.
This can be applied through steam as well by going to properties in the steam menu.
Hope this helps you a little and you get some FPS improvements, if not just replay and il see if I can help you some more