Way too much lag

When I play Minecraft 1.7.9 on my Macbook Pro (10.9.3 Mavericks) it has a very strong lag. For example, when I dig out a block it takes around a minute to actually respond and remove the block and especially when i'm trying to kill zombies they stay stationary for 1 minute and then later they quickly move and I see a very low healthbar due to the fact they've actually been hitting me for the past few seconds but since I couldn't see it while playing due to lag. I've checked my connections with the internet and it seems to be perfect.