Kendall (1945) defines the curve of concentration (AFAIU, this is a synonym for Lorenz curve) as a parametric curve $$ \left\{ \begin{aligned}F(x) & =\int_{-\infty}^{x}f(t)\mathrm{d}t\\ G(x) & =\frac{1}{\mu}\int_{-\infty}^{x}tf(t)\mathrm{d}t, \end{aligned} \right. $$ where $F(x)$ is the CDF of a random variable $X$ with finite mean $\mu=\int_{\mathbb{R}}tf(t)\mathrm{d}t; x\in\mathrm{supp}\,X$. By the way, the expression for $G(x)$ really looks like a ratio of two expectations (times the probability---thanks, @stats_model): $$G(x)=\frac{\mathsf{E}(X\mid X\leq x)}{\mathsf{E}X}.$$$$G(x)=\frac{\mathsf{E}(X\mid X\leq x)\mathsf{P}(X \leq x)}{\mathsf{E}X}.$$
On the other hand, a few sources (here, here) refer to Lorenz curve as “PP plots” of $X$ against a hypothetical uniform distribution---which makes sense, since then its interpretation as representing inequality of the wealth distribution becomes apparent (wealth is equally distributed if x% of the population own x% of it). This, however, contradicts the first definition: $$\left\{ \begin{aligned}F(x) & =\mathrm{CDF}_{X}(x)=\int_{-\infty}^{x}f(t)\mathrm{d}t\\ G(x) & =\mathrm{CDF}_{\mathrm{U}(a,b)}(x). \end{aligned} \right.$$
I find it hard to match the two definitions, and it seems like referring to Lorenz curves as “PP plots” is wrong. Or isn't it?
Kendall (1945): Kendall M.G., The Advanced Theory of Statistics, Volume I, 1945