[2] After Lilja Mósesdóttir left the Left-Green Movement in autumn 2011, she became one of the leading founders of the Solidarity party, along with Sigurður Þ. Ragnarsson.

The goals of the party were listed as using legislation to achieve solidarity and equality, and was described as neither left, right, or center as it wanted perspectives from all sides.

[3][4] Lilja worked as the only Solidarity member of parliament for the remaining part of her term, lasting until 28 March 2013.

[7][8] On October 6 2012, Birgir Örn Guðjónsson was elected the new chairman of Solidarity at the party's national meeting, with Sigurbirn Svavarsson and Pálmeyja H. Gísladóttir as vice-chairmen.

[9] The party decided in February 2013 not to participate in the 2013 Icelandic parliamentary election, but informed they still intended to engage and impact the ongoing political debate in Iceland as much as possible, and thus would continue to be officially registered as a political party with list letter C. They also announced that Lilja Mósesdóttir was elected to once again be chairman, with Rakel Sigurgeirsdóttir as the vice-chairman.