In my opinion, 'brace' is too harsh a word and seems to get people over recruiting their 'six pack' - this is the LAST thing I'd want to see people doing. Summary: six pack is showy and does bugger all for lower back stability and support - not to mention, a dominant six pack OFTEN leads to a 'pooch' in the bikini area of the stomach.
Trouble is, it's very hard to turn OFF the all dominant six pack.
However, see if this helps you:
"Float your navel gently towards your spine -
(about a centimeter)
The word 'float' should enable the lower abdominals to engage without the upper ones firing.
Do this before you perform a movement - be it Pilates, lifting a bar bell, bending over to pick up shopping or even turn around in the car to do up a child's seat belt etc.
As you become more used to this, practice KEEPING the navel floated - you will have to breath sideways rather than into your belly. This is one of the ways you can 'engage the core' to protect your lower back.