For Sony Playstation DUALSHOCK4, Dual Sense, and Nintendo Switch Pro and similar
PSOBB is a game optimized for DirectInput controllers (such as the Sony Playstation DUALSHOCK 4 controller) and most controllers for Nintendo Switch and Playstation. So you should be able to map all the buttons succesfully from the in-game controller setup screen.
For XBOX 360, XBOX One, Xbox Series S|X Controller
PSOBB cannot properly detect Xinput Devices (All Xbox controllers) very well so an external program called XinputPlus. It is required to allow mapping in-game of the LT/RT buttons for Xbox controllers, follow the next steps for a succesful setup:
Download the XinputPlus Application extract it and place the folder into the C:\ root.
Run the program as Administrator (upon first launch you might need to install the .NET Framework, just select download and let it install automatically).
In the main program window at the top you must select the PSOBB Executable (SHPsoBB.exe) located in the main game installation folder.
On the XinputPlus program select the "DirectInput" tab and check the option "Enable DirectInput Output" lastly select under the LT/RT dropdown list the option "Buttons 11/12".
Click Apply, then Quit, then launch PSOBB from the launcher as usual and you shold be able to map the triggers in the in-game control setup menu.
This is a sample screenshot of how the whole setup should look like: