K. this is a great question to ask, & I'm glad you are working with a doctor that is willing to "think outside the box" in helping you treat your migraines.
Here is my story - take it for what it's worth. A few years ago started experiencing swelling in my legs, called "pitting edema". Prior to this, I had been suffering from migraines, fibromyalgia, tmj, borderline high blood pressure, etc. In other words, I'm a bit of a medical mess. =-)
My doctor prescribed a water pill, called hydrochlorothiazide (HCTZ). It works by a different mechanism than Lasix, and is longer-lastsing throughout the day (My understanding of Lasix is it acts in a big whoosh once a day).
The swelling in my legs was finally under control (although I also ahve to be careful with my diet) but even more beneficial side effects were realized -
My blood pressure was finally under control. And the migraines that I used to get 1-2 times a week slowly subsided to once every month or so.
Now... anytime you look up a drug online, you will find the worst of the worst & the best of the best about it. Any side effects or adverse events need to be published by the drug companies in full disclosure. But that doesn't mean they are common, or will necessarily occurr without other symptoms present first.
One of the drugs in many migraine medications is caffeine, which is also a mild diuretic, so taking a water pill is not a treatment without proven results specifically for migraines.
I would talk with your doctor further, & discuss different diuretics available, along with the benefits & drawbacks of each for YOUR situation. HCTZ works for me, but it might not be right for you, due to other reasons. Talking with a community pharmacist might also help you.
Good luck, T.