Low pass filter vs lag compensator?
Yes, of course.

A first order low pass filter with the transfer function \$H(s)=\frac{A_o}{1+sT}\$, has one pole and no zero. Beyond the cut-off frequency and for rising frequencies the attenuation continuously increases.

In contrast, a lag compensator with the transfer function \$H(s)=\frac{Ao(1+sT_2)}{1+sT_1}=A_o \frac{T_2}{T_1}\frac{s + \frac{1}{T_2}}{s + \frac{1}{T_1}}\$ where \$T_2&lt;T_1\$, has one pole and one zero. Hence, beyond the cut-off frequency (pole magnitude) the attenuation also increases \$-\$ however, only until the zero will stop further attenuation and the damping will flatten out (and remains constant).