@myringo, When in doubt, it is always ok to ask.
As for myself, I have my routine labs and Prograf lab done every 3 months now that I'm 14 years post transplant. Since the prograf test has to be before my 8AM meds, I go first thing in morning when my lab opens at 7AM, and I do take a sip or two of water beforehand. Then treat myself to a donut from local bakery to enjoy with a cup of coffee when I get home.

Once a year, I return to Mayo Rochester, for my annual check-up. On that day, my labs are usually 6AM and I di fast from food and water because I have some tests afterwards with a NO food or water directive. On those days, I do still take my meds after the labs with a small amount of water.
@myringo, I'm happy to welcome you to Connect.

When they draw my blood they ask if I’ve had anything besides water or black coffee. I drink a liter of water before I go in. Easier to get the blood out. The phlebotomist appreciates it!