I'm not sure I'm understanding your plans completely.
What I see with the box is basically a nesting box. To be a sheltering coop you would need a roost bar that is not over your nesting area (as you don't want poop on the eggs).
Propping up the lid will ventilate only at the top. Moisture will trap at the bottom. I agree with
@lazy gardener that a good coop area needs bi-directional flow. I'm not sure you'll achieve that with a propped lid.
A good coop design will be:
1. Easy to clean
2. well ventilated for cross flow above the chicken's heads, no direct drafts.
3. area for nesting away from roosting
4. sufficient room at roost to comfortably house birds with wing room...how much can vary, but generally they recommend 2 square feet per bird (if bantam) if they just roost for the night, otherwise you need 4 square feet if they are ever locked in the coop (which from your design they won't be).
I would recommend creating another little box attached to the side for the nest. You would do a cut through from the bigger box for coop to nest access. The little nesting box should be at minimum 12 inches by 12 inches by 12 inches (sorry I can't convert that quickly to metrics...silly American).
I would then put a roosting bar across the bigger box about midway.
I would then "lift" the lid by putting some sort of bracing so that you essentially make a cake tier top with the lid (think pedestal cake, like a wedding cake). I would then fill in the space with hardware cloth or chicken wire.
That will give you a lid that is flat to protect from rain, held up maybe 6 inches all the way around, then wire all around the empty space for air flow above their heads, then a main area below with roosting bar, straw on floor for clean out (you may want to create a drag out access hatch with a cut out that hinges). Then an attached nesting box that the birds can access from the coop.
That should be sufficient for 4 Pekins, if that is what I am correctly assuming by your name....could be for 4 large fowl birds if the box is of sufficient size (I can't tell actual dimensions from photos...it looks a bit smallish).
If you do have the bantam Cochins (Pekins), with their heavy foot feathering, you may want to consider putting bark dust/wood chips on their run area, at least partially, to prevent the inevitable mud they will create. Heavily feathered feet are a magnet for bumble foot if they remain muddy all day long.
My thoughts.
Lovely yard for your birds, btw.
LofMc