I borrowed heavily from this post $20 Ikea Briefcase Bike Pannier, which gives better pictures and more detail than I captured. I just wanted to show how you can take his method and apply it for a different function. I wanted a better way to carry my lunch to class, so I made my lunchbox into a pannier which easily comes on/off.
Pre-planning: Look at all steps to figure out what you need to make happen. I wanted my Ortlieb bag to still work, so I had to make my coat-hanger hooks line up in a way that allowed that bag to clip on. Consider where you are putting your holes in your lunch box and and your where you are lining up your coat hanger hooks if you want to use another bag on your rack.
Step 1: Create Backing/Buy Some Hardware
After cutting away the inner lining of the lunch box, I took an hard plastic clipboard I don't use anymore and cut it to the size of the rear of my lunchbox. I taped the cut edges to soften them so they wouldn't wear into the lunchbox. With only the plastic backing, the bag tended to droop with weight in it, so I cut out a piece of cardboard long enough to wrap around both sides and the back.
Next, I went to the store and bought the following for the mounts:
Two machine screws
4 larger washers (one on each side of the spacer)
2 smaller washers (for the inside/nut side)
I drilled the proper holes, and I assembled my mounts as shown so that the coat hanger hooks will be able to slide into the slot created by the washers and spacer. After my first attempt, I realized I wanted a more solid way to pull the box off of the hooks, so I cut a nylon strap as a handle. I just put holes in each end and slid the strap onto the screws in between my plastic backing and the cardboard.
Step 2: Make Your Mount
I took a stiff wire coat hanger, cut it in half, and worked it around my rack to form deep grooves which my mounts can slide into. I didn't like the idea of the pointy ends catching, so I just taped them up with some black electrical tape. I didn't use a bungee on the bottom yet, so I'm relying on the depth and squeeze of the coat hanger slot to keep my bag from flying out. If that becomes a problem, I may add a bungee on the bottom later.
Like I mentioned earlier, if you want to use your rack for another bag, make sure you plan ahead where to place the coat hanger. I tried to show the way I squeezed it in with one Ortlieb hook forward of the coat hanger and the rear hook in the "lunchbox" slot.
Then Voila, slide in your new lunchbox and you are ready to go.