I'm not sure where she's getting $220 from for Delta.
I flew to America and back to Germany on Delta in February of this year and it was $150 each way. That was with her as a carry on, she sat under my seat.
I just consulted with the Delta website and it is now listing $100 each way, but it doesn't specify if that is just domestic or international.
Make sure when you pay at the check you don't pay in Euro. I had a friend who did that and paid 150 euro. I brought a copy of the Delta policy with me but had no problems and paid in dollars.
BRING HER TO EUROPE! We got our dog here and its great. Europeans are such dog friendly people. At least in Germany you can take them ALMOST anywhere. Restaurants, malls, stores, its awesome. Some countries are a little more strict but if you're coming for three months its worth it.
I don't know if Lithuania requires a health certificate, which would be the most complicated thing because you will need a bilingual one. We got one for our military base. First go to a vet and they'll give her an exam and tell you where the closest USDA office is. Depending on where you live you have to find the closest USDA office to stamp it for you. For me it was only 2 hours away, but I had a friend who had to drive 4 hours.
Also beware, I had the bilingual HC but when I got to the FDA office they told me that I had to have one fully in English which I had to pay $75 for. When I got back to Germany and went through customs she told me ALL I needed was the bilingual one and didn't even look at the one that was completely in English.
I would try just contacting the closest usda office to you, here's their website
www.aphis.usda.gov
hope that helped!