Why is lithium burned at lower temperatures than hydrogen inside stars? The destruction of lithium inside stars through the reaction
$$ ^{7}_{3}{\rm Li} + {\rm p} \rightarrow 2\ ^{4}_{2}{\rm He}$$
takes place at just $\sim 3\times 10^6$ K.
This is much lower than the temperatures ($\sim 10^7$ K) required to turn hydrogen into helium inside stars and is the main reason that lithium is scarce in the universe (e.g., Why is there a scarcity of lithium?).
Given the Coulomb barrier for hydrogen-burning is three times lower than for lithium-burning, why does lithium burn at much lower temperatures?
 A: The lithium-burning fusion reaction rate becomes significant once thermal energies are sufficient for tunneling through the Coulomb barrier between lithium nuclei and protons to form stable helium nuclei.
The first step in the hydrogen-burning (pp) chain features a lower Coulomb barrier between two protons and indeed "di-protons" are formed at lower temperatures than the threshold for lithium-burning. However, the di-proton is unstable, and to produce helium one of the protons must change into a neutron via a very slow weak force interaction before the di-proton decays. This is unlikely, and to have a big enough population of di-protons transforming into deuterons via this weak force interaction requires a much higher temperature (by an order of magnitude) than just the threshold temperature for proton fusion.
In fact a more relevant comparison is the temperature thresholds for lithium-burning versus deuterium-burning. The latter takes place at $\sim 10^6$ K, a factor of three lower than for lithium-burning and exactly what one would expect given the three-times smaller Coulomb barrier.
