The introduction of gain and loss into non-Hermitian systems can induce topological phenomena distinct from those in Hermitian systems, among which the non-Hermitian skin effect and higher-order localized states have attracted broad attention. In this work, we investigate a non-Hermitian Lieb photonic crystal with spatially distributed gain and loss, and systematically study its band structure and topological properties. Finite-element calculations of the complex band structure and finite-supercell eigenmodes, together with a point-gap winding-number analysis, are used to examine the topological properties and non-Hermitian skin effect of the photonic crystal. The results show that higher-order corner-localized states can appear in multiple photonic band gaps, exhibiting multi-gap localization features. As the frequency varies, bulk states gradually evolve from extended states to localized states, showing a pronounced frequency-dependent non-Hermitian skin effect. By analyzing the point-gap topology of the complex eigenfrequency spectrum, we establish a direct topological connection between spectral topology and the non-Hermitian skin effect in Lieb photonic crystals. The results indicate that the sign of the winding number is associated with the boundary toward which the bulk states accumulate, offering an interpretation of the frequency-dependent skin localization. In addition, the introduction of non-Hermiticity lifts the degeneracy of corner states and enables effective control of their spatial distributions. Our results indicate that the lattice geometry of the Lieb lattice is favorable for realizing multi-gap higher-order topological phases and frequency-dependent skin effects, providing a physical basis for the design of multifunctional topological photonic devices.