Note that for $\delta>0$: $\int_{\{\delta \leq |x|\leq 1\}}|x|^{-l}dx=s_n\int_{\delta}^1r^{n-1}r^{-l}dr=s_n\int_{\delta}^1r^{n-l-1}dr,$ and it has a limit $\delta\to 0$ if and only if $n-l-1>-1$ hence $n>l$. So the function $|x|^{-l}$ is locally integrable on $\mathbb R^n$ if and only if $n>l$. If $f$ is locally integrable then it defines a distribution by $\langle T_f,\varphi\rangle=\int_{\mathbb R^n}|x|^{-l}\varphi(x)dx$, and if $f$ is not locally integrable, we don't have a distribution on $\mathbb R^n$, since $T_f$ is not well defined, for examle for a $\varphi$ which is equal to $1$ on a neighborhood of $0$.