  We have analysed optical spectra of BL Lacertae, the prototype of its class,
to verify the presence and possible flux variations of its broad Ha line. We
used the spectroscopic information also to investigate the question of its
parent population. Four spectra were acquired at the TNG in 2007-2008, when the
source was in a relatively faint state. In three cases we were able to measure
the broad Ha and several narrow emission lines. A comparison with previous
results suggests that the broad Ha has increased by ~50% in ten years, a change
not unusual for Broad Lined AGN. We estimated a black hole mass for BL Lac of
4-6 10^8 solar masses from its relation with the bulge luminosity. The virial
mass estimated from the spectroscopic data is instead 20-30 times smaller. We
suggest that this discrepancy is due to the BL Lac BLR being underluminous.
Finally, we addressed the problem of the BL Lac parent population, comparing
its isotropic quantities with those of other AGN classes. From the point of
view of the narrow emission line spectrum, the source locates close to
low-excitation radio galaxies. When also considering its diffuse radio power,
an association with FRI radio galaxies is severely questioned due to the lower
radio luminosity (at give line luminosity) of BL Lac. The narrow line and radio
luminosities of BL Lac instead match those of a sample of miniature radio
galaxies, which however do not show a BLR. Yet, if existing, "misaligned BL
Lac" objects should have entered that sample. We also rule out the possibility
that they have been excluded because of a QSO optical appearance. The
observational constraints suggest that BL Lac is caught in a short term
transient stage, which does not leave a detectable evolutionary "trace" in the
AGN population. We speculate on a scenario that can account for the observed
properties. [ABRIDGED]
