We present L-band spectra of the Be stars γ Cas, f Per, 28 Tau, θ CrB, 66 Oph, o Her, and 28 Cyg, obtained through use of the CID-InSb spectrograph with the 2.1-m telescope at OAN/UNAM San Pedro Martir Observatory. This is the first report of L-band spectra of o Her and θ CrB, and of the data obtained with this spectrograph. We obtain flux ratios of hydrogen lines for these stars, finding that they have optically thin envelopes, except by 66 Oph and θ CrB, which do not show evidence of a circumstellar disk. γ Cas and f Per have flux ratio values of hydrogen lines closer to the optically thick case than the other stars. We use the line flux ratio diagram and optical spectra reported in the literature to study the life cycles of the disks. We find clear evidence of the dissipating process of the envelopes of 66 Oph and 28 Cyg, i.e., they are decaying stars. 28 Tau seems to have passed by a similar process. γ Cas and f Per are stable stars because their circumstellar disks do not show notorious changes for many years. Finally, the stars in a build-up phase, whose envelopes are generated after a decaying phase or for the first time, have not yet been observed in the L-band. It would be useful to monitor more Be stars to observe this class of stars that probably change from a very tenuous envelope to an optically thick circumstellar disk. The line flux ratio diagram seems to confirm that late Be stars have more tenuous disks than early-type Be stars, as they tend to be separated at the left bottom and the top right parts of the diagram, respectively. Larger samples of Be stars are needed to confirm this hypothesis through a statistical analysis.