Suspended graphene provides an example of strongly correlated chiral fermions in 2+1D, and the logarithmic renormalization of the Fermi velocity in the infrared limit is one of the most prominent consequences of electron-electron interaction. For the first time, we could directly reproduce this effect in fully non-perturbative Quantum Monte Carlo (QMC) calculations using as large as 102x102 lattices, which gave us access to the scales approaching those of experiments on real graphene samples. We compared our QMC results with experiment and demonstrated the agreement if the finite-temperature corrections and the screening of the short-range electron-electron interactions by higher bands are taken into account. These results, now validated by experiment, are subsequently compared with multi-loop perturbative calculations made within the Lattice Perturbation Theory (LPT) and in continuum QED. We demonstrate the importance of both lattice-scale physics and diagrammatic corrections beyond Random Phase Approximation for the quantitative description of the Fermi velocity renormalization. We also discuss the finite-temperature corrections, which appear to be of the opposite sign in perturbative series and in non-perturbative QMC signaling about possible breakdown of perturbation theory in strongly-correlated QED.