I am Star Alliance Gold (United MileagePlus) tier for this member. My booking (not using award miles) for an upcoming trip includes some longer waits at airports, so I was wondering if this Star Alliance Gold tier allows me into the lounges of Emirates (at DXB) and Delhi (Vistara).
After doing some research, you should be able to use any “member airline lounge” when you fly a Star Alliance flight while holding the Star Alliance Gold level as you say you hold.
This means that, lounges like Plaza Premium or Al Majlis at DXB will not be allowing you in for free (you can pay to enter those) but you should be able to access any airline member lounge so your only option to access using your Star Alliance Gold membership would be the Lufthansa lounge (they founded Star Alliance after all).
Similarly in Delhi international airport: only terminal 3 has international flights and there only the Air India lounge (part of Star Alliance) should allow you in with your Star Alliance Gold membership.
Generally speaking though, if you fly on business class or first class then that’s a different story because you would then be able to just go to the lounge reserved for business class ticket holders or the one for first class ticket holders depending on your ticket.
Hope this answers your question and have a safe trip wherever you go!