Slow Computer with Updated Lion

http://support.apple.com/kb/HT5048 explains all the benefits of the update.

http://support.apple.com/kb/HT1222 offers better security for 10.7.3 than previous versions of 10.7.

Slowness may be due to lack of hard disk space*:

http://www.macmaps.com/diskfull.html

Incompatible drivers, which may be isolated by booting into safe mode with the shift key.

Spotlight needing to reindex. See my avatar icon, and then look for it in the upper right corner of the screen. Click on the icon in the upper right and see if it says it is indexing. You can stop indexing by adding drives to your Apple menu -> System Preferences -> Spotlight Privacy. This may temporary disable some searching or viewing of the Finder. If all you do is search by file name, Find Any File is a great alternative.

If you have peripherals whose drivers are uncertain, eliminate them one by one to see if there is a change.

If you are using any third party system tools, remove any that aren't associated with backing up. The only "maintenance" Mac OS X needs is backup.