A real lens bends light and can make things look bigger or distort them.
A partisan is a supporter of a cause (not necessarily an unthinking one)
Figuratively "viewing through an XXX lens" is "seeing and understanding the world in the (distorted) way that XXX people do". So viewed through a partisan lens means "seen how partisans would see it".
I guess the suggestion is that the mayor is a partisan (a RepublicRepublican, even though officially the mayoral role is non-partisan) and so you should remember that he has a particular opinion and is trying to get the best result for his "side".