On 23 July 2025, in response to a 2023 request from the United Nations General Assembly, the International Court of Justice (ICJ) issued its seminal advisory opinion on the obligations of states in respect of climate change. The ICJ was of the unanimous opinion that climate treaties impose binding obligations on States to protect the climate system and wider environment from human-induced greenhouse gas emissions, and that under customary international law they must exercise due diligence and use all means at their disposal to prevent activities within their jurisdiction or control causing significant harm to either. This perspective examines the implications of the ICJ’s Opinion for addressing time-lagged impacts (TLIs), specifically sea-level rise above pre-industrial levels (SLR) and cumulative CO2 emissions from permafrost thaw (PFT). We argue that SLR and PFT are clear examples of the ‘significant harm’ identified by the court and find that halting their growth would require net-negative emissions sustained over centuries. This frames the Paris agreement targets as ambitious milestones rather than endpoints of climate mitigation and calls for recognition of long-term international responsibilities for carbon removal—an issue that warrants urgent attention in climate negotiations.