Unfortunately it seems not. 

https://www.lner.co.uk/the-east-coast-experience/first-class/first-class-lounges/

Click the date in the twitter link.

OOI the lounge was not particularly great last time I visited it a couple of years ago, but admittedly much better than the other options.

It is a 1st class ticket valid on LNER services, it should be valid for access to the lounges. I have certainly used passes in 1st class lounges across the UK many times.

Neither of those links actually say otherwise. Sadly passes are often ignored when lists like this are compiled leading fools to infer they are not included until someone in authority bothers to put them back on the list. This cycle tends to repeat every so often.

In practice it will be more about whatever the lounge dragon decides at the time you enter, this applies whatever is written on the company website.

My second link was to a twitter reply from LNER saying it was unlikely. LNER is specific about the tickets it accepts and it does not specifically state interrail/Eurail and in my limited experience I have always had my ticket checked in LNER lounges. I have seen them reject passengers with the really early saver tickets, even though they were valid first class tickets, just not full fare or First advance.

I look forward to anybody with first hand experience or a definitive response from Interrail or LNER.

MY exp also dates from pre-covid, when there was I think not yet that LNER-and there still was Virgin, so it may be much out of date. I´ve always-showing just that 1st cl IR pass be welcomed in all lounges i GB  from whatever company and without need to show RES or other extra things to show. (in other countries it may indeed be needed to show that you plan to use one of their trains in the next 1-2-3 hours). IN the trains I also always got the extra service (food, drinks) that other pax would get. Be aware that GB is fairly unique ion treating its 1st cl pax that way-in fact for the experience I travelled a week around GB enjoying it.

The only review as for now/actual is to try out yourself, I guess