The basic lean-to conservatory has a square or rectangular shape with just a 1-sided sloping roof. The uncomplicated nature of the roof helps a lot to keep the overall cost of lean to conservatories down.
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A typical cheap lean-to conservatory will have a set of French Patio doors and be in the size range of around 3m x 3m.
For bespoke versions of the lean-to, you can rotate the roof angle, so that it goes left to right, right to left, or even front to back.
If you have the room (width) then fitting a set of bifold doors to 2 adjacent sides of the conservatory can give a spectacular “floating roof” effect when the doors are fully opened.