The butterfly and I had lit upon, Nevertheless, a message from the dawn, (31-32)
Hey, look—the speaker's made a buddy. Actually, he's made two. Here he sees himself paired up with the butterfly. The message that he mentions, though, is one that shows him his connection to the mower—and other human beings—as well.
That made me hear the wakening birds around, And hear his long scythe whispering to the ground,
And feel a spirit kindred to my own; So that henceforth I worked no more alone; (33-36)
The speaker's discovery of his connectedness opens up a whole new world for him. He hears the birds around him as if for the first time. As well, his imagination seems to be activated. He "hears" the absent mower's scythe doing its thing, and he "feels" a spiritual connection to his fellow workman. It's amazing what a little connection will do for your mental state.
But glad with him, I worked as with his aid, And weary, sought at noon with him the shade;
And dreaming, as it were, held brotherly speech (37-39)
The speaker's feeling so connected here that he actually takes his lunch break with the imaginary mower. He's not just thinking about him while he munches his Doritos, either. They actually talk (out loud or in his head, it's not clear). The use of the word "brotherly" emphasizes the speaker's newfound frame of mind. He's feeling up close and personal with this mower.
'Men work together,' I told him from the heart, 'Whether they work together or apart.' (41-42)
The lasting lesson of this poem is—appropriately enough—delivered as a communication between two people. This emphasizes their personal connection, and reminds us that the experience is one that's deeply meaningful for the speaker, who tells it "from the heart."