Some smaller fish count towards that RoE also, more specifically silver sharks. Noticed this targeting Titanictus and Ryugu Titans on the Selbina Ferry.
I just want to add since I haven't seen it anywhere yet, Lu +1 can be repaired with woodworking also, just like the NQ. Also once repaired, the rod will lose its "signature". If this concerns you just trade the rod back to the quest giver and he will put the signature back on.
any fish that is caught and does not stack will count toward this
Silver sharks stack, as do nebs which do count towards this objective.
It's really how long you keep the catch on the line until stamina is depleted that determines how many pts are awarded if the catch is successful.