1. The solution to the inequality $\lg x-\frac{1}{\lg x} \leqslant 0$ is
$$
\text { 2.1. }\left(0, \frac{1}{10}\right] \cup(1,10] \text {. }
$$

From the original inequality, we have $\frac{(\lg x+1)(\lg x-1)}{\lg x} \leqslant 0$.
Then $0<\lg x \leqslant \frac{1}{10}$ or $1<\lg x \leqslant 10$.
Hence, the solution set of the original inequality is $\left(0, \frac{1}{10}\right] \cup(1,10]$.