The render distance does little to alter the RAM usage. By default you will load an area of 21x21 (441 chunks) despite how much you are rendering.
How much RAM do you have allocated in the launcher? You seem to be running 32bit java, which means the game cannot use more than 1GB of RAM. Upgrade it to 64bit(as long as you have 3.5GB+ RAM and 64bit OS) and give the game 2GB of RAM in the launcher. You could also use the JVM arguments listen in a sticky in this forum. Just don't bother giving the game more than 2GB, its most likely just going to make the lag worse.