Do I need wall lining between a bathtub and insulation
&quot;Lining&quot; usually refers to a tub surround, not the tile backer board. The scenario where you tile to the top of the lip will cause you to have a large gap that will have to be filled in by some kind of caulking which will increase maintenance(ex. mold, grime, possible cause for leakage in the future). It also is a not accepted practice and takes away from the finished look of the bathroom. Another consideration is the brick wall with studs. That type of older construction has a lot of voids so a little extra work in the beginning gives a lot better result. I suggest you seal up the entire room with backerboard and sheetrock before installing the tub. It will keep mice out too- a common old house issue. If the floor isn't in good shape install a new continuous subfloor first.
Decide what you are using for your walls and tub backer. Choices are water resistant sheet rock, some variation of cement board or one of the lighter weight boards made of foam with a masonry skim coat and mesh face. Sheetrock on most of the bathroom is fine but spend the extra money on either of the last two choices for at least the tub area.
Install the backer board of your choice to within 1/4 inch of the top of the tub lip. Do not let it touch the lip or water wicking will occur.  Install tub directly to stud wall. If your tub can use a ledger board then also install directly to studs(no board behind it) with board above and below it. Many acrylic and steel tubs with a lip can be screwed to the wall by putting a washer head screw directly above the end of the lip. Stainless is best. Not necessary for cast iron.  For extra diligence you can use caulk to fill the gap before tiling. It is crucial that the tub is leveled and shimmed before going any further. A slight backpitch to the wall is preferable to it being pitched away from the wall. Shims should be a solid plastic or something similar. Tile will be installed to but not resting on the tub surface. Waterproofing the floor as stated is not a terrible idea if you're located above a living space and will preserve the subfloor.