I watched a different film production of King Lear, this time with Dame Diana Rigg in it as Regan. Of note is the scene where Regan is newly widowed and cross-examining her sister's servant about Edmund. (If you go looking for it, this scene comes right before the scene where Edgar tricks his blind dad into thinking he has fallen off one of Dover's cliffs.) In the background behind Rigg there is a warp-weighted loom as a prop, with not quite a yard of cloth woven on it.
The loom is free-standing, not propped up against a wall, which is not what I expected from reading Marta Hoffmann's The Warp-weighted Loom. The looms on ancient Greek vases look as though they are free-standing and upright. I'm not sure how the shed would work without the loom being on a tilt. Wish I had one to experiment with.
The warp-weighted loom is a clever choice for a prop in King Lear, a play about a king back in the mists of history, since this type of loom dropped out of use and became an archaic item as foot treadle looms came in.