The baltics doesnt share the timetable because of that you have to search on the local website of Railcompanies 

A good source is even the website of the man on seat sixty one (Man on seat 61) it shows a detailed route description (starting from London but you could read this text from Warsaw and then just do the suggested route backwards. 

There is only on weekend a train service to Poland from Kaunas The prefered kind of transport is still the bus there. 

NO trains over border LT-LV, only for summer/weekends from PL to LT (just 1/day then) and from LV to EE by very bad connection at Valga (dead and nothing to do small village at border).

Passes do not pay off here-local fares much lower. Plus that still reports from EE that conductresses are unable to read QR code and will force you to buy ticket. They should issue a ticket for 0-all tix are sold on board-but about all locals have chipcards or free travel anyway

Not all railway companies share their timetable data with us, but you should be able to find connection by searching directly on their websites. You can find links to all rail carriers over here: Search train times in Europe (interrail.eu) under the section “Why can't I find my journey in the timetable?”

@mcadv 

Please do not spread incorrect information. This train runs during weekends the whole year.