From Förberedande kurs i matematik 1

Because \displaystyle \mathop{\text{lg}} 0\textrm{.}001 is defined as the exponent that should stand in the coloured box in the equality

\displaystyle 10^{\bbox[#FFEEAA;,1.5pt]{\phantom{\scriptstyle ??}}} = 0\textrm{.}001

and we have that

\displaystyle 10^{-3} = 0\textrm{.}001\,,

thus \displaystyle \mathop{\text{lg}} 0\textrm{.}0001 = -3\,.