Precise and accurate mass calibration is required to exploit galaxy clusters as astrophysical and cosmological probes in the Euclid era. Systematic errors in lensing signals by galaxy clusters can be empirically estimated by comparing different surveys with independent and uncorrelated systematics. To assess the robustness of the lensing results to systematic errors, we carried out end-to-end tests across different data sets. We performed a unified analysis at the catalogue level by leveraging the Euclid combined cluster and weak-lensing pipeline (COMB-CL). Notably, COMB-CL will measure weak lensing cluster masses for the Euclid Survey. Heterogeneous data sets from five recent, independent lensing surveys (CHFTLenS, DES SV1, HSC-SSP S16a, KiDS DR4, and RCSLenS), which exploited different shear and photometric redshift estimation algorithms, were analysed with a consistent pipeline under the same model assumptions. We performed a comparison of the amplitude of the reduced excess surface density and of the mass estimates using lenses from the Planck PSZ2 and SDSS redMaPPer cluster samples. Mass estimates agree with the results in the literature collected in the LC2 catalogues. Mass accuracy was further investigated considering the AMICO-detected clusters in the HSC-SSP XXL-North field. The consistency of the data sets was tested using our unified analysis framework. We found agreement between independent surveys at the level of systematic noise in Stage-III surveys or precursors. This indicates successful control over systematics. If this control continues into Stage IV, Euclid will be able to measure the weak lensing masses of around 13 000 (considering shot noise only) or 3000 (noise from shape and large-scale-structure) massive clusters with a signal-to-noise ratio greater than three.