I pinged a complaint over to customer relations about this - and this is the response I got back:
Thanks for your recent email. You’re clearly unhappy that there were no menus available in our Galleries First lounge at London Heathrow. We know how important our lounges are to our customers and I can see we’ve let you down.
We know that our airport lounges are a key aspect of Executive Club membership, and that you greatly value this. We’ve also looked into our own processes to make sure the problems that are reported are dealt with as quickly as possible. We’re grateful you've taken the time to tell us what happened, as it’s only through receiving your comments we know where to focus our attention. I’ve sent the details of your complaint to our Customer Experience team and the Lounge Manager at London Heathrow airport and I'm sure they’ll definitely value your insight.
Absolutely no information - but they've recognised I'm "clearly upset" - and they agree they've let me down - so that's ... not helpful ... if they don't actually resolve it.