That DLL has nothing to do with Lazarus or Freepascal.
You need to download it from mysql.com so Lazarus/Freepascal can access MySQL databases.
1. Go to
http://dev.mysql.com/downloads/mysql/5.0.html#win322. Click on Pick a mirror for the "Without installer" version (win32 or win64 section) whichever Windows you have
3. Click on "No thanks, just take me to the downloads!"
4. Download the .zip file from your closest location
5. Unzip it
6. Copy the libmysql.dll from the /bin directory of the unzipped files to your \windows\system32 directory
7. Delete the unzipped files and the downloaded .zip file itself
8. Done.