Solubility of lead phosphate I've read that lead phosphate is very slightly soluble and so any addition of protons shifts the equilibrium back to the solvated ions. What I can't understand is why the lead phosphate is more soluble in hydroxide or basic solutions also.

Source- Vogel's qualitative analysis
The precipitation of lead phosphate would be due to the following reaction.

$$\ce{3Pb^{2+} + 2PO4^{3-} &lt;=&gt; Pb3(PO4)2}$$ 

In acidic solution the phosphate ions would be protonated, thus reducing the concentration of $\ce{PO4^{3-}}$ and increasing the solubility of $\ce{Pb^{2+}}$.

But the precipitation of the phosphate is not lead's only reaction in alkaline solution.  Lead can also form a hydroxide precipitate. In strongly alkaline solution lead can also form various soluble hydroxide complexes which would reduce the concentration of $\ce{Pb^{2+}}$ thus increasing the solubility of $\ce{Pb3(PO4)2}$.