can anyone suggest some strengthening postures, or a series of asanas to
correct overarching in the lumbar spine?
Initially I would say you have very tight Hip Flexors and possibly Quads.
These are pulling your hips forward at the top (negative thrust) causing the
Lumbar spine to hyperextend.
You don't want to strengthen them, you need to stretch them to 'improve' the
range of movement, not 'maintain' the ROM.
What I am saying is that static stretching, as in Yoga, will not be suffice.
A contract / relax method should be used. (Similar to PNF)