IMHO -but without any guarantee- it is best to check frequently around the 4 month mark as we had many flights where about 4 months out the computer doing the AI yield management for this route decides that the unsold inventory is too high and prices come down and we scored at least 15 to 20 % lower than at earlier dates ... At LH the human factor for yield management seems to have been replaced by AI ...
always good to try to fly on a tuesday or thursday and avoid specific dates when schoolholidays start and every body wants to leave in the same week )