Orphan tools are a bitch. I somehow doubt you'll find anything purpose built. I think you're talking about some sort of sleeve? Even if you find a sleeve, getting it to fit tight and not twist or creep up or down will be a challenge. You could have one made in a machine shop, or you might find a short length of aluminum pipe that about the right thickness, then use shims to hold it tight, or even cut a groove in the router and inside of the sleeve and use a pin to hold it in place.
Another option if you can find it would be to cut the tube in half vertically so that when you clamp down, it grips the router. Sort of like brake shoes in a drum brake.
You're talking about something like a pipe wall about 3/8ths thickness. Not sure if you'll find that off the shelf. I found this site as a place to start. Accessories - Caps/Plugs/Nuts/Sleeves/Finishers - Hard Line Tube Adapters, Tube Nuts & Sleeves - AN Aluminum Tube Sleeves - Page 1 - Redhorse Performance
I'd contact their sales department and ask for exactly what you want. Measure carefully both the loose and tight diameter of the lift for the Outside dimension (OD), the outside diameter of the router housing for the inside diameter. You can always use aluminum sheets to cut extra shims as needed to make everything fit.
Any custom milling you have done will likely cost as much as a new lift. I gave up on lifts (Rockler) and bought a Triton TRA001. Price is now about $260. More than a motor and most name brand lifts, but it has lots of power and a built in lift, as well as good dust collection. My twenty five cents worth.