It's not a problem. You can resort to any type and works with 3rd party stuff like with normal JS code.
declare var fancyNewLib: any;
fancyNewLib('hello');
fancyNewLib.someCoolFeature = 3;
You don't get any suggestions or typechecking (obviously), but you're no worse off than just using JS in that sense. And you can easily replace your 'declare' with the actual // <reference> tag when you find it or make it, and clean up any errors.