Okay, man, you totally lost me there. How do I go about "reinforcing: the edges? I can see WHAT you did, I just have no earthly idea HOW you did it. Care to share?
As with most things in Anim8or there are a few ways to skin this particular cat. One way is to include a few extra points in the initial rectangle before it's lathed (An8-roller-6a). They don't need to be close to the top and bottom edges yet so if you are using 'snap to grid' you don't need to fiddle it down to a superfine setting or anything, just whack them in anywhere but keep them on the same level on each side of the rectangle. After the rectangle is lathed, switch off any grid-snapping and select all the nodes in the horizontal lines created by the extra nodes ('Point Edit > Drag Select'), then drag them up close to the top edge (An8-roller-6b). Repeat the process for the bottom edge.
If you forget to add the extra nodes before lathing you can add them to the cylinder by dragging the 'Point Edit > Cut Faces' tool across the cylinder (tip: disable the axes you don't want the knife to move in). Or you could select all the faces in the roller ends and use the 'Point Edit > Extrude Faces Connected' tool to pull the faces outwards slightly, which has the same effect of doubling-up the edges around the inner and outer rims.
An alternative method that gives a neater, slightly rounded edge is to bevel the edges that you want to reinforce (An8-roller-7a & An8-roller-7b). It can be pretty tedious carefully selecting only the edges to bevel, especially if you want to further reinforce the edge with another bevel, but it's an option.