The thermal expansion and specific heat measurements under ambient pressure and the thermomagnetization measurement under applied pressure for new Lu6(Mn1-xFex)23 compounds have been carried out in order to discuss the relationship between the thermal expansion anomaly and the spin fluctuations. The thermal expansion coefficient α significantly increases above the Curie temperature TC. The electronic specific heat coefficient increases with increasing x, accompanied by the decrease of the spin fluctuation spectral width. The value of the pressure dependence of TC, ∂TC/∂ P, is large at about -50 K GPa-1. The anti-invar effect and the pressure effect of TC are closely related to a significant thermal variation of the amplitude of spin fluctuations.