Unlined vs. Half-lined vs. Fully-lined Suit Jacket Linings
A natural fiber lining on the inside of a suit jacket is a sign of quality.
Bemberg is a natural form of rayon made from cotton linter. It's considered the king of linings as it's durable, relatively inexpensive, breathable, and easy to find.
Silk is a luxury fabric and therefore expensive. Although sought after for suits, especially custom, I don't recommend it is difficult to clean and impossible to fix if torn (you need to replace it). It is breathable though, so an option for hot weather.
Polyester or oil based rayon linings are common in low-cost and mass manufactured jackets – avoid them as they are the least breathable.
The inner jacket lining is usually color-coordinated with the suit fabric. If you decide to go with a contrasting color, it makes the suit more casual (although you can keep it buttoned and no one will know). A lining provides a suit jacket with durability and helps to maintain its line.
An unlined suit jacket is bound to cost more than a suit that is completely lined. Why? Labor and skill – unlined jackets are rare and the artist building the coat will need to ensure his inner stitching is beautiful as the suit jacket's owner will be able to see it.