On the second Thursday of every month, NOAA issues its analysis of the status of ENSO. This includes determining the Alert System Status. Although the current status remains the same i.e. La Nina Advisory, the forecast has been adjusted somewhat from last month. The forecast calls for the La Nina to continue but weaken during the Summer. Then it’s forecast to strengthen again in the Fall and Winter. The timing is shown in the NOAA discussion and the IRI probability analysis.
Of importance, the chances of a Triple Dip La Nina are still difficult to predict but seem to be higher than the estimate last month. I am not exactly sure how you define a Three-Peat. If it has to do with extending into early Winter the odds seem to be a bit higher. This is not likely to change the forecast for Winter but might change the forecast for next Spring. Finally, there is now less disagreement among meteorological agencies as to when this La Nina will end.
So I am referring to it as a Three-peat but it is not over until it is over. So it may not happen but it looks increasing as if it will.