Context. Observations of the γ-ray sky with Fermi led to significant advances towards understanding blazars, the most extreme class of active galactic nuclei. A large fraction of the population detected by Fermi is formed by BL Lacertae (BL Lac) objects, whose sample has always suffered from a severe redshift incompleteness due to the quasi-featureless optical spectra. Aims. Our goal is to provide a significant increase of the number of confirmed high-redshift BL Lac objects contained in the 2 LAC Fermi/LAT cataloge. Methods. For 103 Fermi/LAT blazars, photometric redshifts using spectral energy distribution fitting have been obtained. The photometry includes 13 broad-band filters from the far ultraviolet to the near-IR observed with Swift/UVOT and the multi-channel imager GROND at the MPG/ESO 2.2 m telescope. Data have been taken quasi-simultaneously and the remaining source-intrinsic variability has been corrected for. Results. We release the UV-to-near-IR 13-band photometry for all 103 sources and provide redshift constraints for 75 sources without previously known redshift. Out of those, eight have reliable photometric redshifts at z > ∼ 1.3, while for the other 67 sources we provide upper limits. Six of the former eight are BL Lac objects, which quadruples the sample of confirmed high-redshift BL Lac. This includes three sources with redshifts higher than the previous record for BL Lac, including CRATES J0402-2615, with the best-fit solution at z ≈ 1.9.