...Welcome Paul, so glad you are here! It sounds like a really tough situation there in Lithuana...
Okay, I just googled..entering 'lithuania law for transgender rights' and an article came up...try to search for it, it was on webpage called 'gaystarnews.com' and the date was july 19, 2012. I read it, it does say that gender reassignment surgery is not recognized by law there , nor will you be new papers be given if you receive surgery in another country. It does then go onto say that by the european human rights act that any unmarried person that gender reassignment is medically feasible should receive it. It said lithuania has not passed a new law on this yet though.
To me this says hopefully that maybe lithuania WILL be passing a law to allow for your surgery since it is needed....hopefully sooner than later. I really encourage you to try to find this article as well as other legislations that may have been passed since then. Maybe something has already gone into place?......if not, I would highly consider relocation...maybe on a student visa or something? I'm glad you're here, and hopefully someone will be able to offer up suggestions for you to proceed forward. Good luck, paul!