The safety rule comes first
Do not stop a treatment to make a number look better. Interrupting an anticoagulant, an antihypertensive, an antiepileptic or a thyroid replacement carries a real risk, while the number itself only carried an inconvenience. If a treatment needs holding, the person who prescribed it says so, in writing, and says for how long.
That rule covers the great majority of cases. Most medicines do not need to be paused before a routine panel, and taking them with a glass of water does not break a fast.
The handful that are timed, not stopped
A few treatments are usually taken after the draw rather than before, so the sample shows your ordinary level rather than a peak.
Levothyroxine is the common one: taken that morning, it can lift the measurement and make the reading harder to interpret, so the usual instruction is to take it once the blood has been drawn. The same logic applies whenever a laboratory is measuring the level of a drug itself rather than its effect, which is why those requests often specify a time relative to the last dose.
None of this is a pause. The dose is taken, just later in the morning.
Supplements are a different question
Iron supplements are the clearest case. Taken on the morning of the draw, iron can distort a serum iron measurement, which is why iron studies are usually asked for in the morning and fasting, and why a supplement is worth pausing for a few days beforehand. Ask your laboratory how long, because the answer depends on what is being measured.
Biotin, often taken for hair and nails and present in many multivitamins, deserves a separate mention: high doses can interfere with several laboratory assays, including some thyroid and cardiac tests, and the interference works on the measuring method rather than on your body. Say what you take, at what dose.
The general version: supplements are not neutral just because they are sold without a prescription.
What to tell the laboratory
Bring a list, or a photograph of your boxes. Name, dose, and when you last took each one. Guidance on venous blood sampling treats patient preparation as part of sample quality, and what you take is part of that preparation.
If you did stop something on your own before realising, say so rather than hiding it. A result read as though you had taken your treatment, when you had not, is worse than a result with a note on it.