The main thing wrong with your code, is that you are using the ugly, error-prone, old-style syntax for connecting signals, instead of the new-style syntax.
Here is a re-write of your example code:
self.signalMapper = QtCore.QSignalMapper(self)
self.lineEdit_331.returnPressed.connect(self.signalMapper.map)
self.lineEdit_331.returnPressed.connect(self.signalMapper.map)
self.signalMapper.setMapping(self.lineEdit_331, 'links')
self.signalMapper.setMapping(self.lineEdit_341, 'rechts')
self.signalMapper.mapped[str].connect(self.test)
If you're curious why your original code didn't work, it's because you should have used SLOT in the first two connections. It should have been:
QtCore.QObject.connect(
self.lineEdit_331, QtCore.SIGNAL('returnPressed()'),
self.signalMapper, QtCore.SLOT('map()'))
This is because there are two overloads of QSignalMapper.map, so you would have needed to specify which one you intended to use.