I recently had plumbing repairs in my shower and they had to remove a section of the wall. I discovered that the tub lip in one corner has rusted badly. The rest of the tub lip has little to no rust damage. I plan to install backer board flush with the lip and have the tile hang over the lip as illustrated below. Is there a way to fix the rusty tub lip before I install the tile? Do I need to fix the lip? Do I need a new tub? Thanks.
Rusty steel tubs tend to get worse, not better, nor even stop where they are. When it inevitably rusts more, you'll be ripping out any tiling you do now as well as the old tub.
You can certainly try various rust-treatment nostrums, but I'd suggest just facing the tub replacement now as the more certain path to a tile job that can stay put on a tub that's not going to rot away. I would not suggest a steel tub for the replacement.