Iceland is dear to Lithuanians for being the first new country in the world to recognize Lithuanian independence from the Soviet Union (in February 1991). Merely a year had been passed at the time from independence restoration (1990 03 11) and the Icelandic move (directed by foreign minister Jon Baldvin Hanibalsson) was bold indeed. Soviet Union still considered Lithuania its territory and Iceland had to ensure another source for natural resources in case Soviet Union embargoed it as a revenge for recognition of Lithuania.
Lithuanians organized a "thank you Icleand" action in 2006, hoping to collect 300 000 "thank you" signatures - one for every Icelander. One out of 10 Lithuanians would have had to sign this and while only over 200 000 signatures have been collected this was also impressive. The signatures were presented to the president of Iceland. It is unclear where they are now.
~2006 the number of Lithuanians in Iceland started to increase rapidly.
Lithuania is a country of 3 million therefore even if a large percentage of Lithuanians emigrate somewhere in that location they usually make a much smaller minority. Not so in Iceland: only ~1500 Lithuanians moved there but they are already the Iceland's second-largest minority (after Poles) and makes up 0,5% of total population. However after the 2009 crisis hit Iceland the number of Lithuanians there ceased to increase.
In 2012 direct air route was opened between Reykjavik (Icelandic capital) and Lithuania. The medium haul (2863 km) route is notable for two reasons: Iceland is the smallest (population-wise) country to have a direct air route to Lithuania and this route is also the longest non-stop route from Lithuania. It mainly serves the community of Lithuanian Icelanders.
There are Lithuanian musical groups and a language school for kids. There are no Lithuanian buildings however. There used to be bar "Vilnius" in Reykjavik that had Castle of Gediminas (that exists in Vilnius, Lithuania) as its symbol.
Before WW2 Iceland used to be a remote Danish fishing colony with little non-Scandinavian population. Even then though a Lithuanian citizen Teodoras Bieliackinas used to live in Iceland and write articles on the country for the 1930s Lithuanian press. This personality has been researched in a recently published book.