John not mentioned at tomb in Luke

In Luke, only Peter, and not John, is mentioned to visit Jesus’ tomb.

Luk 24:12 Then arose Peter, and ran unto the sepulchre; and stooping down, he beheld the linen clothes laid by themselves, and departed, wondering in himself at that which was come to pass.

If TDWJL was John, shouldn’t he have also been mentioned by Luke? But, if he was Lazarus, then he would not be considered a significant character since he was not an apostle and a youth.