I forgot to update my solution here.
Picture shows what I did. Specifically, I used 4x2" and fitted them tight against the post, no drilling to the posts. Then I fixed them through the panel onto another piece the other side. I used metal corrugated sheet on top, except in the middle where I used light panels to brighten it a bit and also so the window beneath gets some light. This is a guest room, so does not get used much. On the house side, I chemi-fixed M12 threaded bar and bolted the 4x2" back to the wall plate. All worked out well. My next step is to close in the big gap from the top of the panels to the roof of the lean-to, the wind/rain comes from the west, so my car gets wet one side. I'm considering my options here. Most likely a see-through panel but with a large air gap.
the cable in view is from the solar panels on my garage (not lean-to) roof connecting to the panels on the house roof. You can just see on the right side the up-and-over garage door runner, this is bolted here temporarily to the panel as I need to raise the up-and-over door by 18" and that's a sunny day job with a sheet of ply and fibreglass, this will allow me to fit a roof rack to the land rover as currently, there's 10mm clearance.
The idea is to have a lot of ventilation, I don't want it as a garage, just a dry and shaded place to park my land rover and motorbike (in summer). With the added security of course.
Bonus is, I can walk on it next to the house side and clean my solar panels now and then, also now fitted a pulley type small washing line one end, so we can hang the dog beds/blankets up. I've added a power socket the door end, so now I can fit a battery manager. A very useful feature, even though it don't look fantastic...yet.