Luke is the counterman at the restaurant where Adam stops for a bite to eat along his journey. We don't know much about him except that he's small and thin and always on the phone. Once again, like with many of the other characters Adam meets along his bike ride, these details serve less to characterize Luke than to help us remember him when we meet him again at the hospital. It turns out he's a switchboard operator (which is why he's always on the phone), and sometimes he gives out meals, too.
At the restaurant Luke smiles and gives Adam extra food, and he eventually steps in to help defend him against the bullies Whipper, Dobbie, and Lewis. Notice how the people who, in the end, turn out to be staff of the hospital (as opposed to patients) are kind and helpful to Adam along his journey (like Luke and, as we saw, Mr. Harvester).