LIC is served by 5 subway lines, a commuter rail line with two stations in the area (and a third in progress to serve a new commuter rail connection to Manhattan), a ferry, and multiple bus lines, with various connections between them all. It is one of the best served neighborhoods as far as transit goes, even compared to Manhattan.
And if you want to get there from neighbouring Brooklyn, by itself containing 2.6 million people, you will probably have to go through Manhattan anyway.
Actually the 'G' train, which only serves Brooklyn and Queens, terminates in LIC at one of the major transfer stations (where one can connect to the 'E', 'M', or '7' trains).