Identifying the uniqueness of FeP-based superconductors may shed new lights on the mechanism of superconductivity in iron-pnictides. Here, we report nuclear magnetic resonance(NMR) studies on LiFeP and LiFeAs which have the same crystal structure but different pnictogen atoms. The NMR spectrum is sensitive to inhomogeneous magnetic fields in the vortex state and can provide the information on the superconducting pairing symmetry through the temperature dependence of London penetration depth $lambda_L$. We find that $lambda_L$ saturates below $T sim 0.2$ $T_c$ in LiFeAs, where $T_c$ is the superconducting transition temperature, indicating nodeless superconducting gaps. Furthermore, by using a two-gaps model, we simulate the temperature dependence of $lambda_L$ and obtain the superconducting gaps of LiFeAs, as $Delta_1 = 1.2$ $k_B T_c$ and $Delta_2 = 2.8$ $k_B T_c$, in agreement with previous result from spin-lattice relaxation. For LiFeP, in contrast, the London penetration depth $lambda_L$ does not show any saturation down to $T sim 0.03 $ $T_c$, indicating nodes in the superconducting energy gap function. Finally, we demonstrate that the strong spin fluctuations with diffusive characteristics exist in LiFeP, as in some cuprate high temperature superconductors.
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