Shouldn't be a big issue. You might stand for part of the way of course but I'm sure they won't let you stranded.

My trip went as follows:
The Polish train from Bialystok had plenty of spaces in first class. I entered an empty compartment. The conductor liked my interrail. No question about reservation. All other people, mainly Poles, left in Suwalki, of before, except a couple with an interrail. They had a reservation for the Polish train, but the company that organized their trip did not reserve the Lithuanian train from Mockava, as that was not necessary and there was no first class. When entering we noticed there was a first class compartment, but the conductor forbade us to enter. So we sat comfortably second class and our mobile tickets were accepted. Later I saw the first class was open. The other conductor said something like "yes” when I asked if it was possible to sit there. Arriving in Kaunas the couple left and when I saw that many many people wanted to enter I decided to give them place and move to the compartment "first”. But just when I wanted to sit the compartment was flooded with young executives in their late twenties or thirties, only man, no women, who all looked for the seat number on their paper tickets. So I had to move to a seat that was not occupied. The conductor barked at me that I had to move out, telling me that it was "business class" and threatened with a fine as if she was still a servant of bad old Stalin. "Business class” was the only English she knew, by the way.

Concluding, after more investigation:
The connection Krakow - Warszaw - Vilnius mainly serves local passengers.
The train from Mockava to Vilnius is supposed to have only second class, although there is a 1th class compartment. You have to reserve it but you can't.
Apparently in Lithuania reservation in 1th class is mandatory, in 2nd class not possible.
On the website of Lithuanian Rail I found that with an interrail pass you are supposed to get a ticket with 100% reductiong, but on my train the mobile IR was good enough.

Always good to hear some feedback like this, thanks @hapé !

Thanks thibcabe for your words. I needed them.

Hi! May I ask you a question as I’m traveling on this route this summer? I have a reservation from Warsaw to Vilnius but I guess it’s valid only for the Polish leg. When I change in Mockava where should I seat on the Lithuanian train? Should I just show my travel day ticket to the ticket inspector or should I reserve a seat at the station? I have a 2nd class global pass and I understood that it’s not possible to reserve a seat in second class. Thank you very much!

Hi Klodia88,

As I just experienced (June 20, 2024), you don't have to, and cannot, reserve second class in the Lithuanian train from Mockava tot Vilnius. Just enter the train and find yourself a nice seat. However it might be quite full in midsummer.
First class seems to be meant for hard workers. It's a silence compartment, you shouldn't talk there, and reservation is mandatory. That seems to be the case all over Lithuania.
For the train from Vilnius to Riga probably all seats must be reserved.
When i know more I will mention it here.

Thanks Hapé, I will take the train from Vilnius to Klaipeda, Klaipeda to Siauliai and Siauliai to Riga as next stops I’ll be waiting for your feedback, enjoy your trip!