Theoretical values for the third and fourth ionization potentials of the lanthanide elements from La to Lu are presented. The results are based on large-scale multi-reference averaged coupled-pair functional calculations starting from a complete active space reference wavefunction and single-reference coupled-cluster calculations. Relativistic effects were accounted for by small-core energy-consistent ab initio pseudopotentials. The results obtained for optimized uncontracted valence basis sets including up to i functions were extrapolated to the basis set limit. The importance of higher angular momentum basis functions in ab initio calculations for energy differences between configurations with different 4f occupation numbers is discussed.