Cook pasta according to package instructions.
Heat up the olive oil from the anchovy jar on medium high, plus some extra if needed to make about 1/4 cup total. Dry the capers well, and fry them in the hot oil.
Once they get a little crispy, drain them on a paper towel. To the now-very-seasoned oil, add the garlic and chili flake, along with the anchovies. Bring the heat down to medium and let everything cook out together.
The anchovies will kinda disappear, that's what you want. If the garlic is going too far, bring the heat down some more. If you're using tinned fish, throw that in with the garlic and chili.
With anchovies disappeared and fish warmed through, add a bit of pasta water and stir on medium heat until a nice emulsified sauce is achieved.
Off the heat, finish the sauce with the lemon zest and juice, along with a few drops of fish sauce. Taste, and if you need more fish sauce, go for it.
Top the pasta with the sauce, and sprinkle on the fried capers. Voilà!