Reading previous posts about Star Alliance lounge access at LHR Terminal 1, I was under the impressions I could not get access to the lounge if I were flying LHR->USA on United Airlines unless I had a business class or higher ticket, regardless of my Star Alliance Gold status.

Based on this info, I did a run and shower at Zurich, thinking I could not shower at Heathrow. But when I got to Heathrow, I was able to walk into the lounge with just my *A card and economy ticket.

So, for the record, yes, you can get access to the Star Alliance lounge (and the only showers in LHR Terminal 1) if you are Premier Exec or higher in Mileage Plus.