Why did you install Firebird 32 server on a Windows 64bit machine??
You can, without problems, install Firebird 64bit server on Windows 64bit and still access it with your 32bit Lazarus program.
But now for your problem at hand...
Do you have a WOW64 directory in C:\Program Files (x86)\Firebird\Firebird_2_5_2\ ??
In that case you'll need to do this:
const
LibName: String = 'C:\Program Files (x86)\Firebird\Firebird_2_5_2\WOW64\fbclient.dll'; // <-- this is the 32bit version
But did this not work?
const
LibName: String = 'fbclient.dll';
(If I remember correctly Firebird should register it's fbclient.dll so you don't have to supply a full path to it. And in that case the correct 32bit one is automatically taken from the registry for it.)
(Maybe you can even leave the whole UIBDBase.LibraryName line out)
How would you solve this if your program runs on another machine with a slightly different Firebird client/server ?? The 64bit fbclient.dll should have been copied to the C:\Windows\system32 (for 64bit) and the 32bit fbclient.dll should have been copied to C:\Windows\SysWOW64 (for 32bit) automatically during installation of Firebird.