  Molecular hydrogen (H$_2$) formation and dissociation are key processes that
drive the gas lifecycle in galaxies. Using the SImulating the LifeCycle of
Molecular Clouds (SILCC) zoom-in simulation suite, we explore the utility of
future observations of H$_2$ dissociation and formation for tracking the
lifecycle of molecular clouds. The simulations used in this work include
non-equilibrium H$_2$ formation, stellar radiation, sink particles, and
turbulence. We find that, at early times in the cloud evolution, H$_2$
formation rapidly outpaces dissociation and molecular clouds build their mass
from the atomic reservoir in their environment. Rapid H$_2$ formation is also
associated with a higher early star formation rate. For the clouds studied
here, H$_2$ is strongly out of chemical equilibrium during the early stages of
cloud formation but settles into a bursty chemical steady-state about 2 Myrs
after the first stars form. At the latest stage of cloud evolution,
dissociation outweighs formation and the clouds enter a dispersal phase. We
discuss how theories for the molecular cloud lifecycle and the star formation
efficiency may be distinguished with observational measurements of H$_2$
fluorescence with a space-based high-resolution FUV spectrometer, such as the
proposed Hyperion and Eos NASA Explorer missions. Such missions would enable
measurements of the H$_2$ dissociation and formation rates, which we
demonstrate can be connected to different phases in a molecular cloud's
star-forming life, including cloud building, rapidly star-forming, H$_2$
chemical equilibrium, and cloud destruction.
