If strong electron-electron interactions between neighboring Fe atoms mediate the Cooper pairing in iron-pnictide superconductors, then specific and distinct anisotropic superconducting energy gaps Δ j (K⃗) should appear on the different electronic bands i. Here, we introduce intraband Bogoliubov quasiparticle scattering interference (QPI) techniques for determination of Δ j (K⃗) in such materials, focusing on lithium iron arsenide (LiFeAs). We identify the three hole-like bands assigned previously as γ, α₂ and αⁱ, and we determine the anisotropy, magnitude, and relative orientations of their Δ j (K⃗). These measurements will advance quantitative theoretical analysis of the mechanism of Cooper pairing in iron-based superconductivity.