As far as I am aware there are currently no train links between Lithuania and Latvia.

You can get from Warsaw to Vilnius by train (daytime service, VERY slow, and not too comfortable once you've changed onto a Lithuanian train just after the border). You can then get from Vilnius to Klaipeda, near the Latvian border, on a very fast and comfortable train, but once you're there that's it.

Air Baltic has a good reputation, so if you want to spend time in Germany as well then a Transatlantic flight to a convenient German airport and a separate ticket on Air Baltic might be your best bet.

Or you could use Ryanair for the last leg... but I wouldn't!