There is no straigthforward answer.
Firstly, the mixture lime / water is highly non newtonian, pseudoplastic, so there is no simple definition of what viscosity is.
The following data is extracted from a technical paper
for a commercially available lime milk
23.5% wt (shear stress Pa shear rate s-1):
(0 0) (20 40) (31 200) (40 900) at 20°C
Secondly, a commercial paper displays significant differences, depending on the kind of lime. I do not know to what extent the information is reliable, but the graph shows viscosity going way up at 300 g/l (as ca(oh)2) when prepared by slaking CaO, and the "limit" is 700 g/l when prepared from hydrated (ca(OH)2). The paper states that the lime milk remains "liquid" for less than 200 g/l Ca(OH)2 if prepared from CaO, and less than 500 g/l if prepared from hydrated lime.
Hope this helps, I have quoted here what I found, but would not be overly confident on the above data