Corruption may be the main problem here, honestly. Lack of proper education too.
I was engaged to a Lithuanian, she had to go abroad to study because it was impossible in Lithuania. She would've remained abroad had things not stopped working.
That happens to a lot of people. They go abroad for a few years to study. They find someone and start building a family and never go back to Lithuania as planned
A stronger partnership between Baltic nations regarding education could help covering most if not all fields, and keep people inside.
The military of Lithuania could be improved and methods changed. Someone I know is in the army only for the week end, has never went under proper training and yet is already having officer classes. This is ridiculous, borderline dangerous.
In France, when you enter, you're trained for months to be ready for combat. Physical training, combat training, survival training, military classes (history and military history of the country and France isn't lacking experience). You learn the values of being a soldier in France. You are taught discipline.
That's before you can enter officer classes if I remember correctly, but even then you need some education level and you need to be someone with authority and good discipline, the personality of a leader.
Lithuanians aren't really trained in combat, and none of them see real combat. There are under 100 lithuanian soldiers abroad and they aren't seeing combat.
Lowering corruption (saving money), using EU money to help improving military budget to reach a minimum required, increase military numbers and maybe open a factory or two to start building equipment and vehicles. And of course, design their own things.
Improve education and make the army a proper career, and even send 500-1000 soldiers in an area for peacekeeping and help secure EU interests.
It will create more jobs, and potentially keep people in. Military option is temporary because you can only build the equipment once during a mostly peaceful time. But production could continue to sell weapons elsewhere, or factories could be turned into other kinds of production. Building cars for a company for example, or parts for EU space projects.
That would greatly increase Lithuanian prestige and national pride, as well as keep people in and strengthen Baltic relations and give Lithuania a more important spot within the EU.
Generating money could be done by utilizing more space for farming (think of using new technology and AI to build vertical farms with multiple floors, utilizing the same space while being x4 more productive, and even more by using AI to compensate for lack of manpower). That also means you can educate more people on technological farming and AI/Machine Learning in the Baltics. Develop those fields over there and open technology companies. These projects could be state, EU or privately financed.
If I may add: National pride is great, being patriotic and proud but nationalism hasn't done much good when countries/peoples think themselves superior (WW1, WW2, Balkans in the 90s and the Ukraine war to some extent with Russian nationalists).
(If I have made mistakes regarding military, feel free to correct me because I may be wrong - if you've been in the army or currently are - that's even better)