Lifetime fluid of is a joke. Go ask PML what their definition of lifetime of car is and they will tell you 10 years after they expect your gearbox to start acting up and you to go buy a new car.
Any and all oils breakdown over time especially in city driving of lots of start stop and frequent gear changes. A quick check with your gearbox manufacturer e.g ZF will show a recommended oil change interval. Theres no such thing as BMW oil its all rebadged so they can sell you at a higher price.
For ZF gearbox the oil is ZF Lifeguard oil, you can purchase at Eng Soon for about $30++ /L and should take approx 6 or 7 bottles for a full flush. Remember to get the gearbox filter as well as that should be replaced along with the oil.
If you're complaining about the oil being expensive remember a gearbox is 7 to 10k to replace. Ask around outside workshops quote approx $400-$600 at the top end but if you buy everything yourself it'll save you 20% or so at a reputable workshop.