The cotton from Liberty of London are made with a plain weave, indeed the most basic one (criss-cross pattern).
When today, most of cotton fabrics are made of short and thick staples, those from Liberty of London have thin and long staples. Meaning, concretely, that it is a bit closer to silk, which is much thinker and longer (indeed a yarn). Indeed, “Tana Lawn” refers to Lake Tana (Ethiopia), where a buyer from Liberty discovered those high quality cotton plants.
What does mean long? The staples of an average cotton are cc. 2.5 cm / 1″ long, even less. For the extra-long, it can be 3.5 cm / 1.5″ or more.
The long staples enable to make a thiner and more solid threads. And since the threads are thiner, the fabric is softer, and more dense, though thin. Dense here means weaved with a higher thread count (number of thread per square cm or inch). Basically, it’s the same when comparing sheep wool with Cashmere wool.
This explains why the cotton fabrics from Liberty of London are thin, silky, solid, robust, durable, and even wrinkle / crease less