George is loyal to Lennie in many different ways, even though it is he who, ultimately, is faced with the sad choice of ending Lennie's life for his (Lennie's) own good.
George is fully aware of how he and Lennie have some sort of cosmic connection based on their ongoing loneliness. Basically, they are all that each other has. Yet, a lot of value is placed upon this mutual dependence. This is what primarily motivates George to always be protective of Lennie. The following passage illustrates the extent to which George is true and loyal to Lennie, regardless of their differences, or of the fact that they are not related.
Guys like us, that work on ranches, are the loneliest guys in the world...We don’t have to sit in no bar room blowin’ in our jack jus’ because we got no place else to go. If them other guys gets in jail they can rot for all anybody gives a damn. But not us.
Not only does George fulfill an old promise to watch out for Lennie; he also ensures that Lennie does not allow his clumsiness and inherently-limited intellect to get him into trouble. It is clear that George not always succeeds at saving Lennie, after all, they are in Soledad precisely because of Lennie's troubles in their previous place. Yet, the burden that Lennie may represent is not bad enough for George to continue carrying it, becoming ever-more responsible for Lennie.
George also comforts and motivates Lennie in their everyday talks. Even when he treats Lennie in a way that, to the average person, may seem cruel, he still finds the time to speak of their dream of owning a farm together, of tending Lennie's much wanted rabbits, and to "life off the fat of the land".
When George shoots Lennie at the end of the novel, the reader understands that this choice would have still saved Lennie from a much more cruel and violent death at the hands of Curley and his lynch mob. George is loyal even then. In shock, he turns around and sees his dream dissipating with the death of Lennie. The fact that the reader is never told the fate of George might also be indicative of the fact that George and Lennie are meant to be a dyad; they were simply born to live- and perhaps even die, together.