Though 1.5.1 was supposed to fix lag in Minecraft, lag still seems to be present and a lot of it. I have been able to identify that this is not present in all systems, but is present in a lot. Certain fixes for this have even been uploaded to the Minecraft forums, but most fail to fix the lag present.
For proof of this issue links follow: http://www.minecraftforum.net/topic/1747591-151-lag-spike-issue/
http://www.minecraftforum.net/topic/1740090-horrible-lag-after-151-update/
You can find many other topics on this just by Google searching: 1.5.1 lag. Turning smooth lighting on/off does not seem to reduce lag any bit, and neither does Fast graphics mode. My system, as well as others with this bug, seem to be running some of the latest software. (I have a 2nd generation i5-Processor, 4GB of RAM, over 100GB of empty space, and usually nothing else is running with Minecraft open.) I have even gone as far as limiting RAM in which Minecraft uses, but this does not seem to give me any performance increase. My graphics card is completely updated, and is Intel HD. Chunk loading only seems to reduce the frames by 1-3, but since i am getting such a low amount of frames it is hard to tell the amount of impact it is having. It gets to the point that I am running 4 FPS stable, more FPS info follows:
1.4.7:
80-120 FPS regularly
120+ FPS while looking at the sky/ground
1.5:
2-10 FPS regularly
10+ FPS while looking at the sky/ground
1.5.1:
4-12 FPS regularly
12+ FPS while looking at sky/ground
1.5.1 with Optifine:
6-15 FPS regularly
15+ FPS while looking at sky/ground
As you can see, FPS was significantly higher in 1.4.7 and dropped largely in 1.5. All 1.5.1 did was increase my frames by an incredibly small amount. I currently now have the latest Optifine installed, but I only get a small frame increase from that but it does make the game more bearable. However, a mod shouldn't have to be installed to have a still extremely low amount of frames. 24 FPS is considered as very jerky movement for the human eye, and 30 FPS is considered neutral. It has been proven that anything below 30 FPS is straining to the human eye, Nowadays, 60 FPS is considered smooth and fluid and is no longer straining. Anything beyond that is barely detectable by the human eye, but allows it to actually relax. As of now, Minecraft is completely unbearable.
Lag is not a bug, just the result of running a very complicated game on a not very powerful computer. I am sorry that you have a lot of it.