Let me have hobbits about me that are fat (TT 4.viii.714)

Gielgud as Cassius

In Shakespeare's Julius Caesar 1.2.193-96 Caesar points out Cassius to Antony and comments:

Let me have men about me that are fat;
Sleek-headed men and such as sleep o' nights:
Yond Cassius has a lean and hungry look;
He thinks too much: such men are dangerous.

To anyone moderately acquainted with Julius Caesar these lines are quite familiar, and to say that someone has 'a lean and hungry look' has passed into the language as a warning against treachery. The words function much like a kenning, telling the reader more of a story than the words alone say. Now consider the following: 

Gollum looked at them. A strange expression passed over his lean hungry face. The gleam faded from his eyes, and they went dim and grey, old and tired. A spasm of pain seemed to twist him, and he turned away, peering back up towards the pass, shaking his head, as if engaged in some interior debate. Then he came back, and slowly putting out a trembling hand, very cautiously he touched Frodo's knee – but almost the touch was a caress. For a fleeting moment, could one of the sleepers have seen him, they would have thought that they beheld an old weary hobbit, shrunken by the years that had carried him far beyond his time, beyond friends and kin, and the fields and streams of youth, an old starved pitiable thing.

(TT 4.viii.714)

Thus, even as Gollum's teeters on the brink of repentance we find a hint that he is dangerous and not to be trusted, but at the same time the use of this phrase here deepens the pathos by sharpening the contrast between Gollum, never to be trusted, and Sméagol, shrunken, starved, and pitiable.