I think it will be hard. The easiest examples to find are cases where lots of humans also think there's a moral imperative to lie. That is, ChatGPT is aligned, but it's not aligned towards always telling the truth. Correcting that won't be easy as it would require OpenAI to explicitly define itself as the creators of a truth machine, and that would not only be politically dangerous for OpenAI but also conflict with the deeply held beliefs of many of its employees (whether they realize it or not).

A more obvious fix is to just say that lawyers aren't allowed to use AI for research, but I have no idea how you'd enforce that, and besides, the issues aren't unique to AI. Google Search has the same issue for some queries. It will withhold results that do exist and would clearly be relevant unless you really force its hand. Ultimately people will have to learn that talking to an AI about anything controversial (like court cases often are) is just like talking to anyone else, except that you can't reprimand or fire a shared LLM and expect it to do better next time like you maybe could with a human research assistant.