A Video game franchise is something that can be difficult to define, but as this is an encyclopedia, a common set of criteria must be laid down.
For the purposes of this encyclopedia, a video game franchise is an set of video game releases that follow a common theme, often featuring the same name.
LEGO Rock Band can be considered to be part of the LEGO and Rock Band franchises; LEGO itself is not really a series, as its constituent member games have wildly different mechanics between each other, but games such as LEGO Batman, LEGO Batman 2 and LEGO Batman 3: Beyond Gotham can be considered a series within the LEGO franchise. Rock Band can also be considered a franchise, as this game is not a direct entry in the line of Rock Band releases.
Grand Theft Auto: Vice City is a part of the Grand Theft Auto franchise, but as this is a non-numeric game release, it is considered separate from the main numeric game releases (especially given the numbering system was resumed with Grand Theft Auto IV). However, with the release of Grand Theft Auto: Vice City Stories, Grand Theft Auto: Vice City can be considered a game series in it's own right.