Help me with fixing lthe response lag.

For beginning i will describe my problem. Somehow on my device i have long delay before response of the buttons to the touch. It is about half of second, and it is too long for comfortable and succesful playing. Many apps was used for fixing it, but they only increase FPS and does not help to reduce response time. So i want to know, how to fix this glitch. Without buying new device, of course. Maybe, deep tweaking of the settings or something like this. Ah, yes, my OS is "Android" 4.4.2, phone model is LG D285, if it important for easier finding the way for fixing.

If you know, how to fix it, write here your ways or try to find the reason for this bug.

At last i will describe, what i did for increasing FPS. Only what really worked.
Optimised this game through "GLTools", used "Seeder", cleaned the system, little bit tweaked system settings and moved the game to the memory card.