The phrase, "Their large and lustrous eyes Seem to thank the Lord", was made in reference to the animals.
Who was being referred to?
The speaker is describing the beauty and life-giving power of rain after a dry and dusty period. The poet saw animals, presumably dogs or horses, looking up at the sky with their big, shining eyes, seemingly grateful for the rain.
Therefore, the phrase "Their large and lustrous eyes" refers to the eyes of these animals, who are depicted as experiencing joy and refreshment from the rain.