Where did Noah get the meat to feed the lions, tigers, etc., on the ark?
There were no meat-eating animals on the ark because every person and animal who lived before the Flood was a vegetarian!
"Then God said, "I give you every seed-bearing plant on the face of the whole earth and every tree that has fruit with seed in it. They will be yours for food. And to all the beasts of the earth and all the birds of the air and all the creatures that move on the ground-- everything that has the breath of life in it-- I give every green plant for food." And it was so." (Genesis 1:29-30)
[After the Flood] "Then God blessed Noah and his sons, saying to them, "Be fruitful and increase in number and fill the earth. The fear and dread of you will fall upon all the beasts of the earth and all the birds of the air, upon every creature that moves along the ground, and upon all the fish of the sea; they are given into your hands. Everything that lives and moves will be food for you. Just as I gave you the green plants, I now give you everything."" (Genesis 9:1-3)
After the Second Coming, when Jesus will reign on earth for 1000 years, animals will once again be vegetarian and there will be no more predators or poisonous creatures:
"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. The cow will feed with the bear, their young will lie down together, and the lion will eat straw like the ox. The infant will play near the hole of the cobra, and the young child put his hand into the viper's nest." (Isaiah 11:6-8)