Blackout dates and availability are not the same:
Blackout dates: Dates when no burning of miles is allowed.
Availability: award tickets in Business class are issued in booking class "I" for M&M.
LH/M&M has no blackout dates. I don't know about bmi. bmi might have blackout dates for LH flights. You can only find out from bmi.
Availability: It Is possible for M&M members with enough points to check availability for business class award tickets. But that doesn't mean that you can get an award ticket with bmi miles if 'I' shows availability. (I think 'I' is M&M stock but no Star stock - but I'm not 100% sure)