As the [link|http://www.sadgeezer.com/lexx/prince.htm|Sadgeezer Character Bio] puts it - Prince had a job, and no ordinary job. Basically his purpose of being was to make the life of his subjects as horrible as possible.
If he kills Stanley, then he cannot make Stan's life horrible. I don't think Prince could take the LEXX to blow up planets either, for the same reason. The planet Water was another case - the "endless torture" of Fire & "endless pleasure" of Water balanced each other out, so Prince had to take out Water after Xev took out Fire.