I am curious is anyone has has experience with the weather Riga and Vilinus in the first couple of weeks in October. I wish Rick would cover Latvia and Lithuania in one of his books.
I have no personal experience, but looking at the statistics, it seems like you can expect daytime temperatures to peak at around 15-20°C and you can probably expect some rain.
To answer that type of question I go to timeanddate.com and check the actual daily weather statistics in recent years. I like to check the most recent five years, because there can be considerable year-to-year variation.
Use the pull-down box at the right, just above the graph, to change the month and year displayed. Use the Search box at the top right to change the location to Vilnius.
For precipitation I normally just look at the climate-summary chart to be found in Wikipedia's entries for most cities.
I spent about 2 weeks in Estonia, Latvia and Lithuania on a road trip, in mid-summer - including Riga and Vilnius, but also along the Baltic Coast and offshore islands, all of which were beautiful. In many places the land reminded me of the US Pacific Northwest: green and lush (clear evidence that there's no shortage of precipitation). We experienced a wide mix of weather: some pleasant, warm days with sunshine, some days of hard, relentless, driving rain, some wind and fog, and everything in between. That was in July.
During my pre-trip research, I read many accounts of travelers complaining about slogging through heavy rain for days and soggy conditions even in the "best" summer months. So in October, I would be ready for pretty much anything: could be some nice, sunny days, but I would expect at least some rain, maybe a lot of it. I doubt there will be snow in early October, but winters along the Baltic Coast sound pretty wet and cold. Being near the ocean will moderate temperatures, but the sea ice does freeze there (there's even multiple "ice highways" linking the mainland to several large islands offshore in the Baltic, though I'm sure those won't be open yet in October - but understand that winters there are serious).
For a visit, especially in October, I'd come prepared for pretty much any weather. You probably won't need sunscreen and Hawaiian shirts.