Absolutely! As long as you are lowering your monthly payment there should be no reason for them to not lower it.
Do you currently have MI?
Assuming you meet FHA’s requirements for credit (usually 640 score or so is minimum required), equity (need 3.5% based on a new appraisal), and income requirements (typically total debt ratios of less than 45%, but exceptions are often granted depending on individual circumstances), you should be fine to do an FHA loan. I’ve been writing those for the past month or so almost exclusively at 3.25% on 30 year fixed, and usually have room in the pricing to pay most or all my clients' costs as well. Couple of things to remember: you do need that modest amount of equity, and you will have an upfront fee to HUD added to your loan, as well as an additional monthly fee. Bottom line, however, is that IF you are unable to do a conventional loan, a new FHA will be far superior to your current loan. You don’t mention when that loan was taken out, or the reason that your current lender won’t refinance it, but sounds like you’re not eligible for HARP since neither Fannie and Freddie own your loan. It may well be that your servicer is just that, meaning they do not originate new loans. At any rate, you need to have a detailed conversation with a loan officer who can analyze your situation and give you advice on how best to proceed. Glad to help if you’d like, my number is 314-740-0004 and I write loans in all states.