The Liberal Party is a political party in killer7. It is the opposition to the current United Nations Party government of Japan. Although it was once the dominant party in Japanese politics, following World War II it found itself unable to pay for the rental of its own facilities. Its ineptitude was clear, and in 1954 the UN Party, made up of Liberal Party defectors, used the Yakumo to overtake them in the political arena. Since then, the Liberal Party has played a lesser role in Japanese politics.
After a fusillade of nuclear warheads are launched on Japan, kicking off the events of Sunset, UN Party leaders dispatches two Liberal Party canvassers, Ohta and Kuramoto, to meet with United States liaisons in an effort to convince the United States of Japan's continued usefulness and thus persuade her to deploy the Fireworks missile defence system. This meeting takes place at the KAKU building, a disused HQ of the UN Party. However, the talks break down when one of the participants cheats at the Mahjong game they are playing, resulting in a sudden Mexican standoff and the subsequent death of all four negotiators.
It is unknown what happened to the Liberal Party after the UN Party seized control of the Japan; given its totalitarian stance, it may have outlawed the organization and membership therein. However, the fact that Matsuoka dispatched Liberal Party agents to rendezvous with United States governmental representatives may suggest that the UN Party has under-the-table dealings with its political enemies, so it may have been unaffected.
Although there have been several political parties in Japan that have used the name "Liberal", the Liberal Party referred to in killer7 is likely this one due to its place in history: the 1940s, which is when the Liberal Party in killer7 is mentioned in the timeline. Like many Liberal Parties in Japanese history, it was actually conservative in nature; in killer7, it seems that it became truly liberal due to its most conservative members forming the UN Party.
The real-life Liberal Party went through many mergers over the years since the 40s, eventually resulting in the current Liberal Democratic Party, which is also conservative and is in fact the majority party in real-world Japan. In killer7, it seems that it kept the same name and nature throughout history.
The catalyst for all these changes seems to be when Toru Fukushima received a call as a young man asking him to become an "architect" for the UN Party, as this started the defecting from one party to another, which set up the relationship between the parties seen during the game. For this reason, it seems that the identity of the caller is most likely to be a manipulator who would be interested in affecting the course of human history: Kun Lan.