A possible off-the-shelf starting point is a large refracting telescope objective, such as an achromatic objective lens. For a format this large, you’d size focal length based on the format dimensions you want to cover, especially the diagonal if full coverage is required.

For example, one community suggestion was to look for something around a 3000mm achromatic refractor objective for a 2.4 × 1.2m image. In general, infinity focus occurs when the image plane is about one focal length behind the lens, so your desired 2-4m lens-to-paper distance implies an extremely long focal length lens.

The main challenge is not just focal length, but obtaining an image circle large enough to illuminate the whole sheet. Conventional photographic lenses generally do not cover anything close to this size, so specialty optics such as telescope objectives are a more realistic avenue than standard camera lenses.

If you need a very wide horizontal angle of view at only 2-4m image distance, that becomes especially difficult at this scale, so expect major tradeoffs between coverage, focal length, and brightness.