Armor Stand with lying pose

Unfortunately, this cannot be done with a single ArmorStand. All of the limbs pivot around pre-determined points; you can see this more easily with an ArmorStand positioning tool.

You could however position two ArmorStands in a way such that the legs of one are paired with the body/arms of another, like this:

ArmorStand for body:

/summon ArmorStand ~ ~ ~1 {NoBasePlate:1b,ShowArms:1b,Pose:{Body:[278f,0f,0f],Head:[317f,0f,0f],LeftArm:[270f,0f,0f],RightArm:[270f,0f,0f]}}

ArmorStand for legs:

/summon ArmorStand ~ ~ ~2 {NoBasePlate:1b,Pose:{Body:[180f,0f,0f],LeftLeg:[270f,0f,0f],RightLeg:[270f,0f,0f]}}

Dress them up, give Invisible:1b and NoGravity:1b to them, and then use /tp to teleport them into place: