Context. The characterization of a time series is a powerful tool for investigating the nature of mechanisms that generate variability in astrophysical objects. Blazar variability across the entire electromagnetic spectrum is a long-standing puzzle, and it has been difficult to ascertain the mechanisms at play. Aims. Lognormal variability in X-ray light curves, probably related to accretion disk activity, has been discovered in various compact systems, such as Seyfert galaxies and X-ray binaries. Identifying a similar behaviour in blazars would establish a link between them. Methods. Public X-ray data from the blazar BL Lac are used to investigate the nature of its variability, and more precisely the flux dependency of the variability and the distribution of fluxes.Results. The variations in the flux are found to have a lognormal distribution and the average amplitude of variability is proportional to the flux level. Conclusions. BL Lac is the first blazar in which lognormal X-ray variability is clearly detected. The light curve is orders of magnitude less variable than other blazars, with few bursting episodes. If this defines a specific state of the source, then the lognormality might be the imprint of the accretion disk on the jet, linking for the first time accretion and jet properties in a blazar.