There are still a couple of ambiguities in the description, so I'll try to cover a few variations on what you've described, including a possible alternate approach.
Resin casting as the "finished" item
The question describes the objective of making a small box, similar to a ring box, that will be lined internally. The scenario I'll describe in this first case is that the cast resin result will be the exterior of the finished box, possibly with some kind of finish. So the plug/pattern needs to have an exterior that is smooth and polished.
Just an observation: you show hollow tubes plus flat ends if I understand the description correctly. You may have a reason for keeping them separate, or may be planning to join them prior to making the mold. Just a heads up that this shape is typically cast as a single item when making things like boxes and coasters, so you may not need the flat pieces.
To do this, the mold is made "upside down". The pattern would be just the hollow tube at the full height of the finished box (including the bottom). The mold box is a little higher than the tube to allow for a base layer of silicone that holds everything together, and the tube is hung from the top of the box. The mold around the tube is partially filled with silicone (to above the bottom of the tube), which is allowed to partially cure just to the point that it doesn't flow. Then silicone is added outside the tube to the height of the tube. The inside of the tube is filled with silicone to below the top of the tube, the distance from the top being the thickness of the bottom of the box. The mold cavity will then give you the entire box in one pour.
The answer by fred_dot_u does a pretty good job of covering some of the major options for this case. I'll just reiterate that for the tubing approach, there is a broad range of rectangular metal tubing available in aluminum, brass, and steel, and there should be a common standard size close to what you describe. If you go the clay route, many air dry clays will work or use epoxy clay.
Whatever you use to make the pattern, if you're going for the resin or lucite look, you will need to be meticulous with the pattern surface. You will probably want to polish it to a mirror finish. Anything short of that will show up as artifacts in the casting.
Also be aware that walls that are too thin will be a bear to cast. It will be a challenge to completely fill the wall channel without voids, and trapped bubbles will be a problem, especially if you don't use a vacuum chamber. You will need to use a resin designed for thin castings or it may not cure correctly, and it will need to be very thoroughly mixed. Super-thin walls may not hold up to a lot of handling, especially if the resin is on the brittle side.
Resin casting as a skeleton that will be completely covered
If the resin casting will just provide structure that will be wrapped externally and lined internally, there are a lot more options. The pattern doesn't need to be polished. In fact, an irregular surface will provide better adhesion for gluing the wrapping and lining.
Here are some additional options for making a rectangular tubular pattern.
Start with a round plastic tube of the desired wall thickness and a diameter approximately 1-1/4 times the length of a side. Make a length of wood with a square cross section that matches the box internal size (there may be a standard piece of square trim close to the size you want). Taper one end by rounding off the corners. Soften the tube inside and out with a heat gun at a low setting until the tube is rubbery, being careful not to scorch the plastic. Force the tube over the tapered end and onto the square area of the wood, continuing to apply heat until the tube is in place on the form. Let it cool. Knock out the wooden core. You can make a longish squared tube and then cut it to length to make multiple pieces.
An alternative is to heat shrink sleeves cut from PETE soda bottles (500 ml size for this application; they can be shrunken to roughly half-size). Start with a bottle that has a simple, cylindrical portion, and cut out an overly long sleeve of the cylindrical part (you may get several plugs by cutting to size at the end). Put it over the wood form and go over it all around with a heat gun at the low setting. Keep moving the gun around to heat the whole thing and give the heat time to migrate through the thickness rather than working one spot at a time. This will give even shrinkage for a good form fit and avoid melt holes.
You will need around three layers for a minimum wall thickness. Once the layer is a good form fit, slide another sleeve over it and repeat. With proper heating the layers will fuse together, at least well enough for this purpose. This technique can take a little practice to get it right.
BTW, this technique can be used for other purposes. It will make a strong repair of broken wood handles, and can be used to quickly make adapters for things like vacuum cleaner attachments of non-matching sizes.
Wrap a form to create a tube. Use either a squared wooden form as in the previous case, or mark the square cross section on a wood base, drill clearance holes at the corners, and insert four nails (you want them snug but removable). Use one or the other as appropriate, depending on the wrapping material.
For options that involve glue, you can wrap the wood or nails with baking paper for no-mess release. There are endless materials for making the pattern. For materials that are thinner than the needed wall thickness, make several layers, which can be glued together (the glue just needs to keep things in place while you make the mold; high adhesion isn't needed). Materials you can use:
Strips cut from polyethylene jugs. Warm at the form corners and it will bend cleanly. You won't need any mold release for the silicone.
Wrap a tight coil of cotton twine/string of diameter matching the desired wall thickness (i.e., create a tube of string). Thoroughly saturate the string with super glue (original thin liquid). Do this with good ventilation as it will release a lot of fumes. It will harden into a hard plastic tube. The string ridges will provide a good surface for gluing the box cover and lining.
Similar to above, but wrap several layers of cotton fabric to create a tube of the needed wall thickness. Thoroughly saturate the fabric with super glue. The fabric texture will provide a good gluing surface for the box.
BTW, these string or fabric shells are sometimes made with colored string or colored/patterned cloth and used as the actual exterior surface (a different, alternative look from the cast resin).
Wrap a paper strip to the needed wall thickness. Saturate every few layers with super glue. An alternative is to pre-saturate the paper with slightly water-thinned PVA glue. This can take a long time to dry, though. Card stock will take fewer layers than regular paper but you will need to be meticulous bending around the corners.
Cardboard can be formed around a wood form. If you use cereal boxes or notepad backs, you will need to score or steam it at the form corners to get clean, smooth bends. You will need several layers, which can be glued together with PVA glue. With cardboard (this bullet or the next), either seal the surface (including the edges), with something like PVA glue or super glue, or smear the surface liberally with Vaseline and let it soak in.
Construct a tube from flat stock. If you have a source of very thick cardboard, it can be treated like wood. Cut the sides to size and glue them together. Wood can also be used. Craft sticks that look like tongue depressors will be about the right thickness, and may be wide enough for the height you need. If not, glue two together edge-to-edge. This can be reinforced by gluing a sheet of paper onto each side. The wooden form described earlier can be used for alignment when gluing up the flat stock. If it is important for the corners to be rounded, that can be done with minor sanding.
Make the individual skeletons rather than casting them in resin
If the cast resin boxes will be used only as a covered skeleton, and the reason for casting them is to make just one pattern and then replicate it simply, and you need only a limited number rather than mass production, it may not be worth the trouble. As described earlier, very thin-walled castings are difficult and time-consuming. If you need a lot of them, you would probably want to make a bunch of molds, and silicone isn't cheap. Thin-walled castings don't use much resin, so the casting process will waste a lot of resin, and resin isn't cheap.
If the boxes won't be visible, it may make sense to just make each needed box. A number of the suggestions for making the pattern are quick and cheap to make, and would be plenty strong enough to use as the actual box skeleton. Just for context, the skeleton of many small boxes is just cardboard.