How will metallic lithium react with atomic oxygen? Very high in Earth's atmosphere, there's a lot more atomic oxygen than anything else. Although I'm sure the energies involved in keeping oxygen in this state are an important variable, I'm interested (for now) in what compounds would form. 

Mistake here: should be targeting $\ce{Li2O}$, not $\ce{LiO2}$. Would you get $\ce{LiO}$, then $\ce{LiO2}$? If so, will $\ce{LiO}$ be stable enough to bond with another $\ce{O}$ atom later? I can easily believe that lithium metal will simply erode away faster than a film of oxide could develop, given temperatures in the thermosphere and above. I just haven't seen much chemistry on this, however.
As explained in Long-term ozone decline and its effect on night airglow
intensity of Li 6708 ˚A at Varanasi (25◦N, 83◦E)
and Halley Bay (76◦S, 27◦W) Journal of Earth System Science 120, No. 2, April 2011, pp. 291–300:

$\ce{Li + O -&gt; LiO}$

$\ce{Li + O2 -&gt; LiO2}$

$\ce{Li + O3 -&gt; LiO + O2}$

$\ce{LiO2 + O -&gt; LiO + O2}$

The article gives rate coefficients for each of these reactions.

The article also gives $\ce{Li}$, $\ce{O}$ and $\ce{O3}$ concentrations as a function of altitude for the range 80-99km (85km being considered the lower boundary of the thermosphere)