Liz the Squeak wrote; "Holland, linsey, cambric, fair and Irish are all types of linen, the names derived from the area of flax cultivation or particular style of cloth."
Lawn is one of those awkward fabrics that have changed definitions over the centuries. Originally named for Laon in France, its city of origin, lawn was first introduced into England during the 1560s. [Laon lies fifty miles south of Cambrai.]
When Elizabethan poets wrote of ‘printing my thoughts in lawn’ referring to the popular pastime of embroidering symbolic messages as love tokens, it was an exquisitely fine linen of wonderfully crisp snowy white. In Jane Austen’s day it was still a fine linen or cambric, but by the opening of the 20th century the lawn available was predominantly a fine grade of cotton. www.selvedge.org