flexibility is how much length (stretch) you get in a muscle.
mobility is how much of a range of motion you have around a joint.
sometimes things can be passively pulled (stretched) into positions that can't be attained by voluntary motion (mobility).
holding your lumbar arch is a neural recruitment thing (some people don't get how to voluntarily contract their spinal erectors to get their lumbar arch).
holding your lumbar arch is a pre-requisite for movements like squatting and deadlifting.
what matters now is the mobility (range of motion) you can get out of your hips (while the position of your lumbar spine / your lumbar arch remains fixed).
maybe you will need a stretching component... but work your mobilization, yeah. it is only when you don't have mobility because of a muscular restriction that things need to be stretched. and basically... i've found i don't need stretching for very much at all... but i foam roll / self adhesion release my muscles on a daily basis. over and over again. soft tissue release = instant mobility + flexibility. for me, anyway.