Dobson's former partner complained to the PCC that the article in January headlined "Partners in hate" - about Dobson and David Norris, who were both convicted of Lawrence's murder - had breached her son's privacy.
The woman was identified as Dobson's former partner and the article included the name and age of her son, which she said raised "significant safety concerns".
She said her son had been bullied at school following the publication of the article and that he had no connection to the trial.
The Mirror said it had identified the child on the woman's publicly accessible Facebook profile, and from another relative in an interview.
However, the paper said it had removed the child's name from the online article and "offered an assurance it would not name him again in connection with the story (unless the family identified him themselves) and offered to send the complainant a private letter expressing regret for having identified the child in this context".
The PCC ruled that the article was in breach of clause six (children) of the editors' code of practice, which states that "young people should be free to complete their time at school without unnecessary intrusion".
It also breached clause nine (reporting of crime), which says "relatives or friends of persons convicted or accused of crime should not generally be identified without their consent, unless they are genuinely relevant to the story".
The PCC ruled: "He [the son] was an innocent party, and the newspaper had not contended that he had previously been publicly associated with the crime or the legal proceedings against his father.
"In the absence of any consent, the publication of his name and age in a story about his father's conviction amounted, in the commission's view, to a clear breach."
However, a complaint about a separate article headlined "The Eltham 5: Wags, houses and flash cars", which quoted the woman's reaction to the guilty verdict, taken from her Facebook page, was not upheld.
The woman said she had received malicious emails and had lost her job after the second article had been published. The Mirror said the page was publicly accessible.
The PCC ruled: "The accessibility of a Facebook page, however, could not necessarily provide sole justification for publishing material uploaded by an individual. The commission had to have regard for the nature of the information, and the public interest in publishing it.
"In light of the notoriety of the case, and the continuing controversy that surrounded the lengthy efforts to bring the two men to justice, the commission considered that the newspaper was justified in publishing these comments, which had seemingly been made in an open forum.
"There was a general public interest in examining the reactions of those associated with the convicted men, especially in a case where questions about the influence of culture on the terrible criminal behaviour were so critical, and in the exceptional circumstances of this case, which had led to the two men living freely in the community for years between their original crime and final conviction."
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