Is this switch wired correctly?
It sounds like the original intent was that Switch 1 and Switch 2 were supposed to be 3-way hookups to allow Light 1 to be controlled from two locations. It sounds like this part is working just fine.

My guess is that Light 2 was meant to be operated by Switch 3 from a single location. Whoever wired in Switch 3 thought they could tap into the power circuit someplace related to the Light 1 setup. In the process they did not get the power tap correctly connected from an always connected power source and instead either connected it to the Light 1 load side or into one of the travelers that connect the two 3-way switches.

It is difficult to fully visualize just how this may be miss wired without knowing which other boxes the switch 3 actually feeds from and what the configuration of the wiring there is in each of the Switch 1, Switch 2, Light 1 and Light 2 boxes. It will be important to ascertain just which of the boxes of the 3-way light circuit has the power feed to it. And then if the Switch 3 is not directly wired into that same box it may be necessary to re-wire the Switch 3 box to a valid power feed source.