The recent IceCube discovery of 0.1-1 PeV neutrinos of astrophysical origin opens up a new era for high-energy astrophysics. Although there are various astrophysical candidate sources, a firm association of the detected neutrinos with one (or more) of them is still lacking. A recent analysis of plausible astrophysical counterparts within the error circles of IceCube events showed that likely counterparts for nine of the IceCube neutrinos include mostly BL Lacs, among which Mrk 421. Motivated by this result and a previous independent analysis on the neutrino emission from Mrk 421, we test the BL Lac-neutrino connection in the context of a specific theoretical model for BL Lac emission. We model the spectral energy distribution (SED) of the BL Lacs selected as counterparts of the IceCube neutrinos using a one-zone leptohadronic model and mostly nearly simultaneous data. The neutrino flux for each BL Lac is self-consistently calculated, using photon and proton distributions specifically derived for every individual source. We find that the SEDs of the sample, although different in shape and flux, are all well fitted by the model using reasonable parameter values. Moreover, the model-predicted neutrino flux and energy for these sources are of the same order of magnitude as those of the IceCube neutrinos. In two cases, namely Mrk 421 and 1H 1914-194, we find a suggestively good agreement between the model prediction and the detected neutrino flux. Our predictions for all the BL Lacs of the sample are in the range to be confirmed or disputed by IceCube in the next few years of data sampling.