Like an idiot, I made a medieval-inspired setting without magic, and now a significant plot point means that I need a healer to diagnose rapidly increasing levels of lead in the queen's body without the benefit of modern medical techniques or magical help. They already know that lead is what they need to be on the lookout for, and I've established that this particular healer takes a much more scientific approach than most medical professionals of the time, but I don't know how she could possibly diagnose this. From the research I've managed to do, blood levels don't sound like they'd be the most reliable indicator, since most of the lead would be stored in her bones. Were there techniques for lead diagnosis in the Middle Ages, or a more modern technique that I could tweak and put into the setting? It is a fictional world, so it doesn't have to be true to what was strictly necessary at the time.
Others have suggested symptoms and chemical reactions prove the existence of lead poisoning. Since your doctors are already aware of the dangers of lead, they would likely also be aware of the symptoms of acute lead poisoning, so that's a reasonable suggestion. They might also be aware of the chemical reactions (alchemy), so you can probably also use that...
So why am I writing an answer instead of a comment? Because I want to present to you a third option. Detect lead through its properties. However I have to admit that this could be flawed in reality.
Lead is sweet, and in ancient times, the Romans used it as a sweetener for their wine (supposedly). Today kids also love to eat leaded paint that flakes of walls because it's sweet (and they'll put anything in their mouth anyway).
So now you might be thinking, a food tester might prevent the poisoning, right? Wrong, a lot of things are sweet, so a food tester might not detect it. Apparently, back then everyone was a fan of Bear Grylls, or just loved to drink a nice cup of piss, because medieval times (around the year 1000) it was known that the urine of people with diabetes tastes sweet, this was also known thousands of years before that by several other cultures. Another common thing done in medieval times, until about 200 years ago, was blood-letting.
What I'm trying to say is... since lead is detectable both in urine and blood, your healer should do a nice little taste test of the queen's urine or her blood, as this apparently wasn't uncommon at the time. A lesser doctor might diagnose her with diabetes, but your genius healer connects the dots with the other symptoms and properly diagnoses her with lead poisoning. The levels might be to low to actually taste in reality, (or not, i haven't tried), but I feel like it's close enough to make it not seem unrealistic in a story. Maybe use an animal with a sensitive sense of taste.
A second possibility would be to weight her blood and urine against the same volume of non-poisoned nastiness. However, this might be a very small difference.
The highest levels of lead in blood I could find is 330 µg/dL. A list of LD50's claimed the lowest dose of death as 450 (no unit, but taken orally)... considering that Wikipedia states quite severe symptoms for blood levels of above 100 µg/dL, including coma, I'll go with 450 µg/dL as the LD50 (which your queen could survive with a likelihood of 50%). So that would only be a difference of 4.5 mg/L ... rather hard to detect with medieval scales. Maybe the blood/urine could be boiled off so a finer scale could be used. I think that bleeding more than a liter of blood would be a risk in itself (At 3 1/2 liters the likely cause of death for George Washington), but urine would be fairly easy to gather in more reasonable quantities which could then be boiled off for easier measurements.
edit: put emphasis on the fact that this might not be as realistic as other answers due to a comment
There are a bunch of chemical reactions that are used to test for the presence of lead ions (Pb2+). If your healer has some scientific experience and knows he's looking for lead, then he might have stumbled upon one or more of these during experiments with lead. This page lists a few reactions, as does this one, most of them require only relatively basic anorganic compounds that shouldn't clash with a medieval tech level. For your purposes the detection based crystal formation of the lead salt might be better, than identification based on the colour of insoluble precipitates, since crystal structures are very unique (it also makes the test take longer).
In any case the accuracy of his test will be improved a lot if he uses positive and negative controls — so blood that he actively poisoned and blood that isn't poisoned. These words are only used in modern science, but the practice of checking for them can easily be used by a scientifically working healer as well.
Note that many of these reactions would probably fail horribly in a real world scenario for blood level lead detection due to 'contamination' of the blood with all kinds of different metal ions and the low concentration in the blood. You can handwave most of these problems with the testing procedure of your healer (he can at least remove all the organic compounds, and is maybe able to concentrate the metal ions).
The simplest and most efficient way don't need blood test. You just need to diagnose few symptoms like high blood pressure, constipation, sleep problem and stomach pain. Then you just send the patient to different place and change his diet to get rid of possible lead sources.
Of course this is not specific as you don't target lead and lead only but if your story mean lead you will have lead healing.
One of the main mechanisms by which lead poisoning manifests in the body is by disrupting the formation of hemoglobin which transports necessary iron around the body in the blood and leads to anemia which its production is impaired.
Even today, initial diagnostic screenings for lead poisoning often target iron-deficiency to identify the need for a follow up test, rather than testing for lead directly.
I suspect that there are a variety of medieval technology class tests that could be used to identify anemia (such as fatigue and pale or yellow skin) which while non-specific would indicate lead poisoning when found in association with other non-specific symptoms of lead poisoning such as tremors and cognitive impairment.
Before there were fancy tests, one could demonstrate lead toxicity by observing basophilic stippling in red blood cells, observed through a microscope. from http://studydroid.com/printerFriendlyViewPack.php?packId=474391
In Principles and Practice of medicine, Osler describes this appearance of the red cells. More importantly for your medieval doctor (who might not have a microscope), he describes lead lines. from https://books.google.com/books?id=ldqgekrDIdkC&pg=PA386&source=gbs_toc_r&cad=4#v=onepage&q&f=false
The clinical scenario (encephalopathy, constipation, pallor from anemia) with the lead lines might be enough to make the diagnosis. If he has a microscope and can demonstrate the basophilic stippling that nails it.