Rare annihilation decays of $P$-wave spin-triplet quarkonia into lepton pairs proceed via a two-photon intermediate state and suffer from infrared (IR) divergences. We identify the physical root of this IR divergence and its resolution as analogous to the Lamb shift in QED. In this Letter, we provide a complete solution to this IR problem by incorporating the higher Fock component of the ${\chi }_{cJ}$ state, {}, a $c\bar{c}{(}^3{S}_1)$ pair accompanied by a very long wavelength photon. By combining the contributions from the leading and next-to-leading Fock states, we obtain IR-finite and factorization-scale-independent predictions for the leptonic widths of ${\chi }_{cJ}(nP)$. The Bethe logarithms associated with these exclusive decays exhibit distinct features from those in the Lamb shift. Using several influential quark potential models, we find that the predicted leptonic widths of ${\chi }_{cJ}(nP)$ are sizable, indicating promising prospects for observing $e^{+}{e}^{-}\to {\chi }_{cJ}(1P,2P)$ at BESIII. Furthermore, future observations of $e^{+}{e}^{-}\to X(3872)$ will provide crucial insights into the $c\bar{c}$ content of the $X(3872)$ meson.