I think many people overestimate the differences between Badiou and Lyotard, due to an incomplete vision of Lyotard’s work. On the question of innovation, Lyotard is favorable to innovation under the regulation of an Idea, and not some autotelic innovation for its own sake.
It is true that Lyotard hesitated on the best way to express this Idea. In JUST GAMING he invoked the Idea of the plurality (to the point of incommensurability) of language games. He sought for the best way to be faithful to the infinity of the Idea and resist its instantiation in a finite presentation. He diagnosed capitalism as being based on the “instantiation of infinity in the will”, leading to the ceaseless pursuit of novelty and/or performativity.
Badiou in the chapter on Lyotard in his POCKET PANTHEON Badiou declares his agreement on these two notions of plurality and the infinite, even if their analysis of them differs: “The important point, after all, is to retain the ontological sovereignty of the multiple, and to call it the infinite.”
It is also impotant to remember that Lyotard wanted to resist the exclusive temporal focus on the future that innovation so often implies. Lyotard’s counterweight was to place an equal emphasis on anamnesis as a means of interrogating the criteria and values that innovation exemplifies and so often conforms to.