Lion installs a recovery disk by default on your computer, so you can troubleshoot and re-install the OS without having to download it again.
Simply start your computer while pressing Command+R. Your mac should now boot using the recovery disk, where you have several utilities to help you troubleshoot your computer, including the Lion Installer.
You can re-install Lion without erasing any of your files, which should be the way to go, though you also have the option to format your disk using Disk Utility before installing.
For more info, I strongly suggest you visit this link:
If your computer is slow, though, I suggest you check other stuff first. Check what apps are running in the background using the Activity Monitor (found under Applications > Utilities), and get rid/uninstall of any third-party unnecessary apps that might be using too much memory.
You should also have a look at the apps that open at login by going to System Preferences > Users > Login Items. Also check how much Disk Space you have left: If its less than 10-20% of the original I strongly suggest you clean up a bit.
Hope it helps!