The yellowish color isn’t lining, lining is only in aluminum cans because it’s cheaper and easier than using thicker aluminum and is usually clear (unless stained). The lining is what gives the cans structure, usually made of epoxy and/or bpa plastic. Without the lining, you can tear a soda can like double thick tin foil. No need for lining in a steel bottle.

The yellow/golden color on the inside of your bottle is just the metal being stained. Stainless steel isn’t really stainless, just harder to stain because the chromium in it forms its own layer of oxidation that protects from being directly touched. Best guess is that the lemon you put in your water breaks down that oxidation layer before you can drink enough, then the lemon and vitamins/minerals/coloring in the tablets stain the metal