Greetings, I'm Don in Samut Prakan near Bangkok.
Your lime tree is probably not so big that you cannot reach all the foliage, so one way to control the caterpillars is to remove them by hand, with a rag or a cotton glove, or a water spray.
Or the plant can be sprayed with wood vinegar (available at HomePro or Global House in the garden section and other garden centers and farm supply shops), they also have neem oil concentrate (sadao) which is a natural botanical insect repellent. These need to be repeated weekly.
Or you can use a commercial insecticide like those in aerosol spray cans for ants and cockroaches, at Lotus or Big C and neighborhood shops.
I can't tell from the photo of the leaves if the plant is lime (manao มะนาว) or kafir lime (makrut มะกรูด), there appears to be a secondary lobe forming which would indicate a makrut. If makrut then the leaves are used for cooking and you may not want to apply a pesticide, even an organic one, that may contaminate the taste. Therefore you may prefer to use the mechanical control, hand removal or washing with a strong get of water.