Just looked at the Bmi website and for LBA it says "Bmi business lounge", so I fear that is out of date.

Then I checked what it said under "our services" and "business class":

UK Domestic and Western Europe (regional services)
Choose from fully Flexible Business or Business Saver fares to suit your travel arrangements.

You can expect:

Priority seating at the front of the aircraft
Advance seat selection at time of booking
bmi Business Lounge access, where available
Priority Check-in

So even Silver members get access yet people on a business class fare don't? Madness.