Lighting fixture: 2 live, 2 neutral, no ground - Is is okay to have the 2nd neutral used as a ground?
This seems to be an old wiring system. What is on the other end of the white wires? Maybe one of the white wires   was used as PE= Protection Earth=Ground already, but it was not marked yellow-green with shrinking tube or other reliable markings at both ends which is mandatory nowadays.

Otherwise a Neutral must not be used as PE for safety reasons. If both white wires are Neutral and none of them can be re-marked and re-used as PE, best way would be to only use lamps that are isolated and do not need PE, i.e. are having the 2 squares (small square inside 2nd square) as symbol (Schutzisolierung, Schutzklasse 2). 

Yes, Neutral and PE are connected, but only very upstream close to the location where the incoming provider line is entering the building and at one and only one location. Neutral and PE must not be connected anywhere downstream, and are to be kept separated downstream.

If Neutral and PE are connected at a 2nd (or even 3rd, 4th etc.) downstream location, GFCIs (RCD, Fehlerstromschutzschalter ) could be failing, and sensible electronics may be more likely to fail, since a second connection of Neutral and PE would produce a loop which is an "antenna" resp. 1-turn secondary coil capable to catch distortions (50Hz humming) and will be more likely to catch high voltage surges (from lightning strokes nearby, switching activities at the provider's net etc.).