Contrary to popular belief, live lobsters are muddish-brown in color. They turn red only after cooking. If your lobster order arrives cooked or pre-cooked as requested, it will naturally be red. If the lobster is moving its legs, tail, claws or antenna, it's still alive. If when holding the lobster in the air, its tail flaps up and down it's still strong and survived shipping very well.
Live lobster have incredibly powerful claws and can be dangerous.
Even so, the back motion muscles of the claws are week enough to be held by these restraining devices. Since lobsters live in salty ocean water, they will die if immersed in fresh or standing water. Also, be careful not to let your fingers go below the tail. The under part of the tail shell has some sharp edges as well. If the lobster is flipping its powerful tail, this may be dangerous.