This system is for Torchon. Different styles need different calculations.

First of all, here is a list of thread equivalents that I use in deciding which thread to use.

http://lynxlace.com/learningbobbinlace-basics.html#threadsizes

Second as for thread match to grid size. Look at the footside of the lace and measure how many spaces per 2 inches (sorry I still use inches, not cm) -- not pins per inch, but spaces per 2 inches.

(We are actually measuring the size graph paper the design was drawn on. In torchon the mesh is dotted every other line.) So we are measuring the distances between the pins on the footside, which is usually a straight line. The numbers refer to the number of spaces, not pins, in a 2 inch segment of footside.

8/2 inches use cordonnet cotton 40

11 per 2 inches use tatting cotton #70

12 per 2 inches use tatting cotton #80 or Campbell's linen #70/2

6/2 or 7/2  inches use cordonnet #20, pearl 8, Lizbeth 20

5/2 inches pearl 5 

Third: the formula for changing. This will tell you how to reduce or enlarge your pattern to match the thread you want to use. It is a matter of converting the fractions of Second above into decimals to make a simple ratio/proportion equation.

So you have to multiply  what you have times x (unknown number) = your goal or

have x = goal       x = goal/have

So then we have to convert these "per 2 inch" distances into decimals. We are actually measuring the distance between the lines of the original graph paper. Once we have the distance between pins or graph paper lines on the original, and we know the distance we need for the thread you want to use, we can do a ratio/proportion problem to figure out how much to enlarge or reduce.

These numbers below measure the distance between lines on the original graph paper, in decimals of an inch.

8 = 1/8 = .125

11 = 1/11 = .0909

12 = 1/12 = .0833

7 = 1/7 = .1428

6 = 1/6 = .166

5 = 1/5 = .2

So, suppose you have a pattern with 8 spaces per 2 inches, which would be perfect for Cordonnt 40 (Lizbeth 40). And this is too small for Lizbeth 20. You will need to enlarge 6 per inch.

have times x = goal                 Hx = G       x = G/H

x = goal/have        X is the number to enlarge or reduce the original pattern size to get a size that fits with your thread.

For 6/inch    x = .166 /.125        x= 1.32    

Enlarge to 1.3 times original size  (for a moderately dense lace)

For a looser less dense lace    x =.2 /.125      x= 1.6  Enlarge to 1.6 times original size 

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Thread size numbers can be very confusing.  Crochet is usually worked on a relatively coarse scale compared to traditional bobbin lace or needle lace.  Crochet cotton 30 is a little thicker than a pearl 12.  But machine threads 30 and 50 are much finer, and comparable to the sizes of quilting threads.  So here are some equivalents (or similars) that I use.  Each line are  rough equivalents, coarsest first.  A is coarsest, E finest.

A: crochet cotton #30, DMC Cebelia #30, Anchor or DMC Cordonnet #30, Fresia linen 30/2

B: crochet cotton cordonnet #40 DMC or Anchor, pearl 12, Sulky 12, Aurifil 12, Bockens linen 35/2

B+1/2:  crochet cotton #60, Bockens linen 50/2, Moravia linen 40/2

C: Cordonnet 80 (tatting cotton), Fresia linen 80/2, Egyptian cotton 40/3, Brok cotton 36/3

D: Aurifil 28, Sulky 30, DMC Retors 30 or Broder machine 30, Brok 36/2, linen 100/2, Madeira Tanne 30

E: Aurifil 50, Sulky quilting cotton 50, DMC Retors 50 or Broder machine 50, Bockens linen 90/2, Fresia linen 120/2, Egyptian or Brok cotton 60/2, Brok 100/3, Madeira Tanne 50

Not everybody will agree with my equivalents in all the details.  But these are equivalences that I use in bobbin lace.  

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There might be an easier way for somebody who thinks in cm, but my brain hurts.