We observed the gravitationally lensed blazar JVAS B0218+357 with the KVN and VERA Array (KaVA) at 22, 43, and 86 GHz. The source has recently been identified as an active gamma-ray source up to GeV/TeV energy bands, rendering a unique target for studying relativistic jets through gravitational lensing. Here we report the first robust VLBI detection and imaging of the lensed images up to 86 GHz. The detected mas-scale/parsec-scale morphology of the individual lensed images (A and B) is consistent with that previously seen at 22 and 15 GHz, showing the core-jet morphology with the jet direction being the same as at the low frequencies. The radio spectral energy distributions of the lensed images become steeper at higher frequencies, indicating that the innermost jet regions become optically thin to synchrotron emission. Our findings confirm that the absorption effects due to the intervening lensing galaxy become negligible at millimeter wavelengths. These results indicate that high-frequency VLBI observations are a powerful tool to better recover the intrinsic properties of lensed active galactic nucleus jets, which therefore allow us to study the interplay between the low- and high-energy emission.