We report a de Haas-van Alphen oscillation study of the 111 iron pnictide superconductors LiFeAs with T(c) ≈ 18 K and LiFeP with T(c) ≈ 5 K. We find that for both compounds the Fermi surface topology is in good agreement with density functional band-structure calculations and has almost nested electron and hole bands. The effective masses generally show significant enhancement, up to ~3 for LiFeP and ~5 for LiFeAs. However, one hole Fermi surface in LiFeP shows a very small enhancement, as compared with its other sheets. This difference probably results from k-dependent coupling to spin fluctuations and may be the origin of the different nodal and nodeless superconducting gap structures in LiFeP and LiFeAs, respectively.