The molar enthalpy of mixing (Delta H-mix(m)) in the LaI3-MI (M = Na, K, Cs) liquid systems was measured over the whole composition range at 1060 K with a Calvet-type high temperature microcalorimeter. The mixing of two liquid components was achieved by using the "break-off ampoule technique". The dependence of the interaction parameter on composition lambda = A + Bx + Cx(2) + Dx(3) (x = mole fraction of LaI3) was determined. Unknown molar enthalpy of mixing (Delta H-mix(m)) in the LaI3-LiI. and LaI3-RbI liquid systems was calculated using the conformal solution theory of Davis. In all systems under investigation the enthalpies of mixing are negative except the LaI3-LiI system at LaI3-rich compositions. The minimum of enthalpy is shifted toward the alkali metal iodide-rich part and is located at the composition of x(LaI3) approximate to 0.35-0.40. Measured and calculated molar enthalpies of mixing were compared with the molar enthalpies of mixing in the LaCl3-MCl and LaBr3-MBr (M = Li, Na, K, Rb, Cs) liquid systems.