Okay lwj didnt play wuji to sizhui when he was little, sizhui remember wuji because wwx played it when he was little and I HAVE PROOF

Exhibit A: Jingyi doesn't recognize the tune. It's not heard often in Clud Recesses
Exhibit B: Sizhui doesn't recognize the tune. If LWJ played it for him, he would know it was LWJ because he only had contact with him after 3 years, so he was 7. He remembers everything from 7 on

Exhibit C: Lan Wangji himself tells WWX that he hasn't EVER played that song to anyone, which is why it's such an effective way of recognizing him.
Exhibit D: WWX plays it in three situations.
1. He's nostalgic and missing LWJ and he's secluded with nothing else to do while the

juniors are working. This is a common mood for him in the Burial Mounds, so he probably used to play it a lot.
2. He's trying to calm Wen Ning down. He chooses this tune as a calming tune because it was what calmed him down on the cave. A-Yuan is a child and Wen Ning is a

unstable puppet if WWX isn't careful back in Burial Mounds, so it's very likely that he played it for both of them to calm them down, if not to calm HIMSELF down.
3. He's like "what should I play now?" when he and LWJ are going around on Little Apple and he plays that.

It's really his favorite song, he plays it all the time.

Sizhui doesn't quite remember when he heard it because he has amnesia, but he heard it in Burial Mounds.