Regarding how animals suffer -- death is an intellectual abstraction, and an animal doesn't fear an abstract idea of course, doesn't think of it, doesn't get anxious about it, but just has emotions from instincts generally. They fear predators, but don't fear death. They don't suffer the way humans do generally, where a human can feel emotions such as sadness at their own dying, or peace about it. For an animal, they seem to be more in-the-moment, living each moment without regrets or disappointments and so on.
But about the Tiger and the lamb, there are words about this --
5 Righteousness will be his belt
and faithfulness the sash around his waist.
6 The wolf will live with the lamb,
the leopard will lie down with the goat,
the calf and the lion and the yearling together;
and a little child will lead them.
7 The cow will feed with the bear,
their young will lie down together,
and the lion will eat straw like the ox.
8 The infant will play near the cobra’s den,
and the young child will put its hand into the viper’s nest.
9 They will neither harm nor destroy
on all my holy mountain,
for the earth will be filled with the knowledge of the Lord
as the waters cover the sea.
Isaiah 11 NIV
and
1 Then I saw “a new heaven and a new earth,”
a for the first heaven and the first earth had passed away, and there was no longer any sea.
2 I saw the Holy City, the new Jerusalem, coming down out of heaven from God, prepared as a bride beautifully dressed for her husband.
3 And I heard a loud voice from the throne saying, “Look! God’s dwelling place is now among the people, and he will dwell with them. They will be his people, and God himself will be with them and be their God.
4 ‘He will wipe every tear from their eyes. There will be no more death’ or mourning or crying or pain, for the old order of things has passed away.”
Revelation 21 NIV
That perfect world is one to be realized, brought about. He will make it so.