Yes, it does appear that there is going to be internet access in Lithuania.  

I did some research on the possibility of WiFi hot spots in Lithuania.  Lithuania has made a great effort to open up a number of WiFi locations, so you can easily access the internet.  But, I've seen free WiFi advertised at international locations and then have not been able to access it, and others tell me the same. So, we won't really know until we get there. 

Lithuania WiFi  The first link below is the Lithuania WiFi page that lists hot spots within Lithuania and Vilnius.  If you click on the "Hotspot Zones" bar it will bring up a number of places in the city that you can get WiFi access from.  Most of these are free, including the Sarunas where the team is staying.  The hotel that the "others" such as myself are staying in is not listed, but since it isn't sure that we have a reservation there, we may be elsewhere anyway.

City Hot Spot  The second like is City HotSpot which is sponsored by a local company that does web hosting, etc.  It looks like they have hot spots around the city that you can access where you see the City Hot Spot sign.  There are detailed instructions on how to access through their hot spots, and I saw that there is a registration box on the page, so I entered a user name, and voila, they came back with my username and password.  I have no idea if it means that I am really registered and can really connect, but I can give it a try when I get there.