Final answer:
Gerta's motive for being friendly to Anna at lunch is driven by his kind and thankful nature, as well as his desire to distance himself from his current situation.
Step-by-step explanation:
Gerta's motive for being friendly to Anna at lunch can be attributed to his kind and grateful nature. As described in the text, Gerta is a creature whose heart is filled with good cheer, and he becomes more joyful as he eats. He envisions himself becoming the lord of a scene filled with luxury and splendor, and desires to distance himself from his current situation, including the old schoolhouse and anyone who patronizes him.