Lufthansa´s regional airline is called CityLine. They operate a jet fleet of ARJ 85 and CRJ 100 and 200.
Some of Lufthansa´s franchisees, flying under "Team Lufthansa" operate the Dash 8 series:
Augsburg Airways 100/200/300
Cirrus Airlines 100
None of them has the 400 series, even though Augsburg Airways have ordered them.
Tyrolean have the 400 series. They are part of LH´s Star Alliance partner Austrian Airlines group and operate with LH on a code share basis.
To my knowledge, they haven´t had any problems with the 400 series.