is it necessary to kill the lizard spy for this?
Yes.
It is written at the start of my Guide:
Keep in mind: it's impossible to have a romance with Thane and Nauxus at the same time without at least one dead person. Killing the Spy is the best option. Period. If you don't care about the Nauxus Romance and his emblem and want to save everyone; you can play the pure Thane Route.