Reticella lace was created by sewing linen to a piece of parchment with a lace pattern drawn on it. The threads would be drawn from the linen leaving only equally spaced horizontal and vertical bars. The threads would be embroidered and then the lace pattern drawn on the parchment would be embroidered over the bars. It was common in the latter half of the 16th century.
One of the first pattern books containing true reticella patterns was Singuliers et Nouveaux Pourtraicts, published in 1587 by Federico Vinciolo in France.
A book with patterns for embroidery over open squares of linen that were smaller than the reticella squares was created in 1550 by Mathio Pagano. It was called Giardinetto Novo Di Ponti Tagliati Et Gropposi per Exercito e Ornamento Delle Donne.
When later, more open forms of needle lace were created, they did not replace the earlier forms of lace. The earlier forms of lace were still being created and used. This is why it is difficult to date 16th century lace to a more exact date within the 16th century.
Many books with embroidery and lace patterns were published in the 16th century. Lace patterns from one book would appear in anther, even if the other book was published years later in a different country by a different auther. An example of this is the pelican in her piety pattern from Singuliers. This pattern is also included in Corona delle Nobili et Virtuose Donne published in Italy by Cesare Vecellio and also in A Schole-House for the Needle published in England in 1632.
The pattern books cannot be used to date the earliest time a lace pattern appeared. According to Santina Levey in Lace, A History, the pattern books contained 'tried and true' patterns because they were designed for the amateur, not the professional lace maker.
Cutwork was usually made with white linen thread although there are a few examples of the lace worked using colored silk. Most of the lace displayed in museums are the finest examples of their collections. Some museums have cutwork made with coarser thread that they do not have on display.
Here is a link to an online facsimile of Singuliers et Nouveaux Portraicts: http://www.pbm.com/~lindahl/vinciolo/
Here is a link to an online facsimile of Giardinetto Novo Di Ponti Tagliati Et Gropposi per Exercito e Ornamento Delle Donne: http://www.cs.arizona.edu/patterns/weaving/books/ngl_lace.pdf
Here is a picture of someone in the SCA wearing a cutwork partlet. The partlet was made with 16th century lace pattern. The ruff was made using a 16th century bobbin lace pattern from Le Pompe worked in needle lace. The partlet and the ruff were worked in 80/2 linen thread.