Sounds like your lag time is due to loading data files from the hard drive. That is most often the biggest bottleneck on a system. You may benefit from an SSD in this situation, or a better hard drive.
I play Tomb Raider 2013, starting with Normal settings then bumping up textures to ultra and detail to high, etc. On my A10-6800K with no dedicated graphics card I'm getting 60fps (vsync) and dropping to 45fps in heavy situations like the shantytown battles. Using an SSD to eliminate the lag, and there is very little lag or stutter in the game. (Of course, I'm OCd to 4.8GHz, and use 2133MHz memory as well, which helps, with the GPU bumped to 1085MHz for playing Tomb Raider, and run it 720p. I don't get those FPS on 1080p.) Minecraft isn't near that demanding.
The only times my game stutters or lags is during game saves, which are saved to my HDD and not my SDD. Picked up an 120GB Kingston HyperX SSD for $80 on sale. While most 450GB drives I've seen are 15000rpm SAS drives and perform quite well, they just can't match what an SSD can do unless you put them in an array.