Certified GKH Gardening Expert
Yes, that is the chrysalis of the beautiful Giant Swallowtail butterfly, the largest butterfly in the U.S. Its caterpillar eats the leaves of its host plant, citrus. Its feeding won't kill your lemon tree and the leaves should grow back. You may want to get some other host plants in the citrus family to divert them from your lemon tree.
Here are some other host plants:
herb rue - Ruta graveolens
Prickly ash – Zanthoxylum americanum
Hop tree – Ptelea trifoliata
Here is info and a photo of the Giant Swallowtail and its caterpillar.