We denote by $L(x,y)$, $I(x,y)$, and $L_r(x,y)$ the logarithmic mean, the identric mean, and the Lehmer mean (of order $r$; $r$ real) of positive real numbers $x$ and $y$, i.e., \[ l(x,y)=\frac{x-y}{n(x)-n(y)},\qquad xeq y,\quad L(x,x)=x, \] \[ I(x,y)=frac1e(x^x/y^y)^{1/(x-y)},\qquad xeq y,\quad I(x,x)=x, \] and \[ L_r(x,y)=\frac{x^{r+1}+y^{r+1}}{x^r+y^r}. \] The aim of this paper is to present sharp upper and lower Lehmer mean bounds for $L(x,y)$, $I(x,y)$, $(L(x,y)I(x,y))^{1/2}$, and $\frac12(L(x,y)+I(x,y))$.