Botox for chronic migraine has made my eyebrows droop badly. Would a brow lift be suitable in this situation?

I believe you are getting injection in your forehead without getting any injection in your glabella. When we inject the elevator of the forehead without injecting the depressor of the forehead, we cause serious eyebrow ptosis. Many neurologist who do injections for migraine, are not cosmetically savie. I hope that clarify your issue. Ask them to inject the glabellar area as well next time you get injected and decrease the frontalis muscle injection to as minimal as possible.

Botox can be a wonderful solution for migraines and tension headaches in select patients, and it's nice to hear that you are finding benefit with this.
When neurotoxins are placed in the frontalis muscle (across the forehead), a side effect may be a droopy brow. This is because the frontalis is the only brow elevator muscle. So, weakening this function allows the depressor muscles to be unopposed in action.

Since you're dissatisfied with the results, you have a couple options.
One option is a chemical browlift where the neurotoxin (Botox) is placed underneath the eyebrows. By weakening these depressors, you may have a 1-3mm elevation of your brow. This may be enough for you.
If this doesn't look like it's sufficient, or you want a more permanent solution, then a browlift may be ideal.