bmibaby & bmi regional are owned 100% by bmi, so changes in ownership from SMB/LUFFTY/SAS TO Lufthansa (80%) and SAS (20%) will not in its self have any effect.
As to what plans Lufthansa has for baby or regional time will tell, but i wouldn't expect WW3 to break out overnight, i can see Regional doing more feeder work in to FRA, but it only works if you are flying longhaul East bound.
As long as baby don't loose money i think they are safe for now, the heavy checks are all done by Lufftytech now which is a good way of moving money from the UK to Germany and as with most LoCo the cash flow is very positive as result of forward booking up to 6 months in advance.
Lets see what happens when they are in the driving seat in March