Here is the FAA guidance.
(d) Instrument ratings issued. A person who holds an instrument rating on the foreign pilot license issued by a contracting State to the Convention on International Civil Aviation may be issued an instrument rating on a U.S. pilot certificate provided:]
(1) The person's foreign pilot license authorizes instrument privileges;
(2) Within 24 months preceding the month in which the person applies for the instrument rating, the person passes the appropriate knowledge test; and
(3) The person is able to read, speak, write, and understand the English language. If the applicant is unable to meet one of these requirements due to medical reasons, then the Administrator may place such operating limitations on that applicant's pilot certificate as are necessary for the safe operation of the aircraft.
My reading of this is that you cannot add an FAA IR to a 61.75, you have to have the rating on your foreign license to have it added to a 61.75.
The choices appear to be to get a Lithuanian IR and get it added to the 61.75 or to get a standalone FAA certificate and do the FAA IR. That course would require TSA approval.