In the UK, we have a crime of "Misconduct in a Public Office". Should it be used to prosecute politicians who have knowingly lied in order to pursue a personal agenda?

If their behavior adversely impacts the performance of the functions of that office, yes, it would seem the very basis of that law.

In other places, I believe they call this plain old corruption. At the very least, it should present a material case against one's suitability to hold office, although there is no law against simply lacking personal integrity.