Crab is Lance's beloved dog. According to Lance, Crab also happens to be an ungrateful little cur. When Lance announces to his family that his job as Proteus's servant is taking him away from home to the Duke's court of Milan, his family is devastated. The dog? Not so much.
I think Crab, my dog, be the sourest-natured
dog that lives: my mother weeping, my father
wailing, my sister crying, our maid howling, our cat
wringing her hands, and all our house in a great
perplexity, yet did not this cruel-hearted cur shed
one tear: he is a stone, a very pebble stone, and
has no more pity in him than a dog: (2.3.1)
Lance's relationship with his dog seems like a parody of the romantic relationships between the play's couples, don't you think? Crab, like Proteus, is loved and adored but he's not very loyal. (Dogs are supposed to be sad when their masters' leave. Just ask Argos, Odysseus' faithful hound in the Odyssey.) Lance, on the other hand, is loyal to a fault. (Kind of like Julia. We could also compare Lance and Crab to Proteus and Valentine.) In fact, Lance even takes the blame when Crab gets caught "a pissing" under the table at the Duke's place (4.4.1). Lance's reward for his devotion to his pooch? Not so much as slobbery kiss from Crab. Instead, Lance takes a beating for supposedly wetting his pants. Ah, the things we do for love.
Fun Fact: In the film Shakespeare in Love, Queen Elizabeth I's favorite part of Two Gentlemen of Verona is the "bit with the dog." Go to "Best of the Web" videos for a link to a great clip from the film.