Yttrium silicates are promising candidates for environmental and thermal barrier coatings owing to their excellent high-temperature performances. Previous works have experimentally attested to their low thermal conductivity, nevertheless, the experimental data were significantly affected by measurement inaccuracy and the existence of defects such as point defects, dislocations, grain boundaries, and pores in measured samples. In this study, the temperature dependences of intrinsic lattice thermal conductivities of γ-Y2Si2O7 and Y2SiO5 are predicted based on the first-principles calculations of crystal structure, elastic moduli, Debye temperature, and Grüneisen constant. Both silicates display very low thermal conductivities over the range of 300–2000 K; and in addition, Y2SiO5 exhibits relatively lower thermal conductivity than γ-Y2Si2O7. We also show certain discrepancies between experimental and theoretical thermal conductivities, and it strengthens the important role of theoretical prediction of intrinsic lattice thermal conductivities of promising materials.