You can close the Process Lasso GUI/app, so long as you leave the core engine service (processgovernor.exe) running. You will be asked about this when you exit Process Lasso. If you don’t see the message box shown below when you exit, try resetting saved ‘do not show again’ settings via the menu item ‘Options / General / Reset Do Not Show Again Memory’.
Process Lasso Core Engine Shutdown Query MessageBox