Just a fellow Lithuanian chiming in. Don’t even try to take a train from Lithuania, as they are still aligning the rail to the European routes, so International travel is almost impossible. Take a plane out and later you can travel by train.
If you are traveling in summer, even Lithuania has so much to offer and then you could allocate like 3-4 days per City. So say 4 days Lithuania, 3 days in Paris and then similar thing in Brussels, Amsterdam or wherever. We often do long weekend trips to various capitals of Europe and usually it’s enough to catch the vibe and see main spots.
They could be touristy, but they are for a reason, usually they are worth seeing