Lead(II) nitrate is an inorganic compound with the chemical formula Pb(NO3)2. It commonly occurs as a colourless crystal or white powder,unlike most other lead(II) salts, is soluble in water. Lead(II) nitrate can be obtained by reaction of lead(II) oxide with nitric acid ......When concentrated sodium hydroxide solution is added to a nitrate solution, basic nitrates may be.....Simple Pb(OH)2 is not formed up to at least pH12. For more details consult https://en.wikipedia.org --wiki

I suggest as references:

J.L. Pauley, M.K. Testerman, "Basic salts of lead nitrate formed in aqueous media", J. Am. Chem. Soc., 176(16) 1954, 4220–4222;

G. Todd, E. Parry, "Character of lead hydroxide and basic lead carbonate", Nature, vol. 202, 1964 (25 April), 386–387.

You need to get a good water chemistry book - either the one by Stumm and Morgan (Aquatic Chemistry) or Morel and Hering (Principals and Applications of Aquatic Chemistry). These books have Tables for all the solubility products of comment salts (the Ksp for Pb(OH)2(s) is 10^-15.3 for example) and complexation constants (for soluble Pb(OH)+ for example. From these values, you can calculate the pH you need to have (by adding NaOH) to precipitate Pb(OH)2 to the desired level. Note that Pb(2+) also forms a complex with 3 hydroxides (Pb(OH)3-, so if you raise the pH too much, you will have an increase in the concentation of this complex. You should draw a pC-pH diagram for Pb(OH)2(s), similar to the one for Fe(III) shown on figure 5.1 of Morel and Hering's book. Do this by combining all the equilibrium equations so that each soluble species is written in terms of the solid (Pb(OH)2(s), whose activity can be assumed to be 1, and plot the resulting relationships. (Like Figure 5.1). Note, this will be at theormodynamic equilibrium, and amorphous precipitated have higher solubilities, but it will tell you the pH dependencies.