From 1st July on weekends. @rvdborgt  posted the timetable fewdays ago.

FROm Kaunas only on sat-sun. It is a rather long trip with many changes and I suppose you do not really want to visit obscure little POlish towns like Suwalki or Bialystok. Bite the bullit and book yourself on an overnite BUS from Vilnius to Warszawa-plenty and not overly expensive.

I see youre suomenlainen-be also prepared for more hickups before from Hel via EE and LV-NO trains at all as for now LV-LT. Maybe beter to not activate pass untill you reach Poland and use/pay for bus till there-saves a lot of time and stress