To add to others who cares who they are its show me the money...
Knowing there intended use can help e.g. they want it for a brand yes that can mean it has high value to them but doesn’t mean anyone else would see it as the same value now or ever?
You can start with asking them why and if the law firm is acting for a third party? They may not tell you then again they may? Not sure what legal disclosure rights are? Formal or informal etc
Check owners of other TLD’s and cctlds, prices and when they sold, if there developed if they are check tax returns, Turnover Company’s information etc Google the word not just g com but, de. co.uk .jp etc and other search engines also, check word meaning in other languages? Check acronyms, abbreviations, companies called the same word or similar. look for patterns of similar words or owners of them, Google the lawyers name, there company, there address etc see if there it comes up with any one they represented etc check there linkedin etc Any new patents, trends, inventions etc you can try and negotiate conditions of sale + % of future increase in sale over 1. 5. 10 years etc
You could do all this and more and draw a complete blank if your boss is trying to squeeze them then really he should think of employing a specialist negotiator or someone who knows what rocks to look under e.g. private detective etc rather than asking someone who doesn’t...