Security Update 2013-003 keeps failing to install - 'Unexpected Error occurred' - and now my MacBook Pro is running extremely slowly?

I have repeatedly tried to update the software 'Security Update 2013-003' on my MacBook Pro OS X Version 10.7.5 but it keeps failing to install, stating that 'an Unexpected Error Occurred'.

Since the update failed the first time, my MacBook Pro has been running extremely slowly and failing to open basic apps like Mail and Safari at times.

All other updates have been successful apart from this one. I have made sure that my MacBook isn't full (emptied Trash etc) but it still runs really slowly at times so I think it's linked with the Security Update failure.

Please help!

*I have tried installing the update from Support Downloads but it says there isn't space on Macintosh to install it. There is 190 GB of free space on that disk so I don't understand that at all.

LION system.