I think that there are specific contexts in which Steinbeck uses the imagery of animals to illuminate Lennie's traits. These images are employed to give a visual reference point to how Lennie should appear in the reader's mind.
Some of the first animal imagery that Steinbeck uses to describe Lennie would be in the exposition of the narrative. Consider the opening description of Lennie as a bear when he first enters:
Behind him walked his opposite, a huge man, shapeless of face, with large, pale eyes, and wide, sloping shoulders; and he walked heavily, dragging his feet a little, the way a bear drags his paws. His arms did not swing at his sides, but hung loosely.
In employing the imagery of the bear, Steinbeck helps to illuminate Lennie's size. In specific comparison to George when they both enter the brush, using the "paws" helps to accentuate the size of Lennie and the size of Lennie's hands. As Lennie "dabbled his big paw" in the small pond, one is able to visualize Lennie's size and how everything in front of him seems tiny and vulnerable in comparison.
Another example of animal imagery that Steinbeck uses is found later on in the first chapter. After George discards the dead mouse that Lennie found, Lennie retrieves it. In confronting Lennie about surrendering the mouse, Steinbeck employs the image of a dog to describe Lennie at this moment:
George’s hand remained outstretched imperiously. Slowly, like a terrier who doesn’t want to bring a ball to its master, Lennie approached, drew back, approached again. George snapped his fingers sharply, and at the sound Lennie laid the mouse in his hand.
The use of "terrier" is significant. It shows that Lennie, despite his overwhelming "bear" size, is actually extremely loyal to George. Akin to the dog, Lennie obeys George as a dog does a master. The detail of "who doesn't want to bring a ball to its master" is another example of animal imagery that evokes how much Lennie is dependent on George. The idea of how a dog obeys its master no matter what is something that will be seen again in chapter 3 with Candy and in the final chapter in the brush with George and Lennie.