We investigate the thermoelectric properties of the relatively unexplored rare-earth ternary compounds La3Cu3X4 (X = Bi, Sb, As, and P) using first principles electronic structure and Boltzmann transport calculations. These compounds, of which the La3Cu3Sb4 and La3Cu3Bi4 have previously been synthesized, are all predicted to be semiconductors and present a wide range of bandgaps varying from 0.24 eV (for the Bi compound) to 0.87 eV (for the P compound). We further find a mixture of light and heavy bands, which results in a high thermoelectric power factor. In addition, as discussed in our previous study (Phys. Rev. B 95 (22), 224306, 2017) at high temperatures of 1000 K these compounds exhibit lattice thermal conductivity less than 1 W/mK. The combination of low thermal conductivity and good transport properties results in a predicted ZT as high as ~1.5 for both La3Cu3P4 and La3Cu3As4, under high p-type doping. This predicted high performance makes these compounds promising candidates for high temperature thermoelectric applications and thus merits further experimental investigation.