If the soil is lifeless then you need to add life.
You may want to get a hose-end aerator and go over the area just to get the soil breathing (they make mechanical aerators but I'd imagine it would be very expensive for such a small area - unless you plan to aerate your entire lawn).
Whether or not you aerate, the next step would be to put down a thin layer of good compost and use
dry molasses in the amount recommended to stimulate the existing biological activity in the soil. You might also want to try one of the
thrive products. It is my understanding that though the labels mention different products (tomato, vegetable, flower) the product in the bottle is the same, a boost of mycorrhizal fungi that also stimulates the good biological activity in the soil.
Am amendment like lava sand will help your soil hold more water if drying out is a problem (in addition to not enough light).
Good luck with that.