The fact that your ancestor left Lithuania after 1940 and before 1990 can be a little more difficult to prove. The Lithuanian consulate website will sound very strict on this information, but I want to assure you that it didn’t seem to make that much of a difference in my case.
It seems that this information can be proved by way of other documents. For example, my mother’s birth certificate would prove that my grandparents had left Lithuania long before 1990. I was initially worried that there was no actual proof that they had left AFTER 1940. All documents I have other than their birth records are dated after 1940, but I thought, “who is to say they didnt leave in 1938 and i just did not include those documents?”
However, this never became an issue for me. I simply submitted all the documents I had, and it was enough.