We present high-level ab initio calculations for the global adiabatic potential energy surfaces of the ground state ((X) over tilde (2)A') and several excited states ((A) over tilde (2)A', (B) over tilde (2)A", (C) over tilde (2)A', ($) over tilde (2)A', and (E) over tilde (2)A") of LiFH, including the valleys leading to Li+HF and LiF+H. The ab initio calculations were carried out using the multireference singles and doubles configuration interaction method with 99 reference configuration state functions (CSFs) for the (2)A' states and 39 reference CSFs for the (2)A" states. The basis set consisted of 140 contracted Gaussian functions, including specifically optimized diffuse functions, and calculations were performed on a dense grid of similar to3500 nuclear geometries which allowed us to construct an accurate analytic representation of the two lowest-energy LiFH potential energy surfaces. An analytic 2x2 quasidiabatic potential energy matrix was obtained by fitting physically motivated functional forms to the ab initio data for the two lowest-energy adiabatic states and explicitly including long-range interactions. The newly presented LiFH fit is compared to several ground-state LiFH fits and one excited-state LiFH fit that have appeared in the literature.