Little Red uses Terminal 1 at LHR, which is in a complex with Terminal 3 and with the former Terminal 2 which was torn down and is now being rebuilt.

I used Little Red in the opposite direction, flying down from EDI, and traversed Terminal 1, which is the "domestic" terminal at LHR. I did not see a VS lounge there. I doubt that you could access Terminal 3, where the VS Clubhouse is, on your "Little Red" ticket.

I would allow 45-50 minutes to get from Terminal 4 to airside at Terminal 1. You will have to take the train which runs underneath the landing field at LHR to get from Terminal 4 (which is south of the field) to Terminal 1-3 (which are at the northeast side of the field). The train only takes 5 minutes or so, but when I've gotten to the train platform at T4, which is a 5 minute walk from the exit from customs, I've had to wait up to 10 minutes for the train. Then, when you get off at the T1-3 station, you'll have to walk close to 10 minutes through a pedestrian tunnel/walkway to get to the security entrance. Then, add on whatever time it takes to go through security; if you don't qualify for Fast Track, you might have a 15-20 minute wait.

As far as Little Red is concerned, I had a very nice experience with it. Check-in at EDI was quick and easy, and they put a Fast Track sticker on my BP which saved me 15 minutes compared to the regular security line there, even though I bought the ticket separate from my TATL ticket and had no status on VS. The plane was clean and the FAs were friendly. The flight only was about 60 minutes.