Here, that’ refers to the song of the grasshopper.

In summer, all the birds get tired and feel drowsy in the terrible heat. Therefore they stop singing and seek refuge under the shade of the cooling trees. To continue the music of nature, the Grasshopper ‘takes the lead’ and makes the poetry of earth alive, with his merry voice. The scorching heat of summer cannot deter his happiness and he keeps on singing until he gets tired. 

The poet considers the Grasshopper as the poet of summer. Therefore he personifies the Grasshopper. He uses a capital letter to describe the role of the Grasshopper in hailing nature. The Grasshopper teaches us to enjoy the poetry of nature to the fullest.

“.. he takes the lead.” Who is ‘he’ here? When does ‘he’ take the lead? How?

Here ‘he’ refers to the grasshopper. He takes the lead in summer.

In summer, the extreme heat makes the birds, the choir of nature, so exhausted that they become silent and take rest in the cool shades of the trees. Just then when the poetry of earth seems to come to a standstill, the grasshopper takes the lead. The grasshopper joyfully moves from one hedge to another, taking the lead in ‘summer luxury’. He becomes the poet of summer who, when tired rests in weed for some moments and again continue singing happily with energy, delight and vigour.