  During a period of strong $\gamma$-ray flaring activity from BL Lacertae, we
organized Swift, Neutron star Interior Composition Explorer (NICER), and
Nuclear Spectroscopic Telescope Array (NuSTAR) follow-up observations. The
source has been monitored by Swift-XRT (X-ray Telescope) between 2020 August 11
and October 16, showing a variability amplitude of 65, with a flux varying
between 1.0 $\times$ 10$^{-11}$ and 65.3 $\times$ 10$^{-11}$ erg cm$^{-2}$
s$^{-1}$. On 2020 October 6, Swift-XRT has observed the source during its
historical maximum X-ray flux. A softer-when-brighter behaviour has been
observed by XRT, suggesting an increasing importance of the synchrotron
emission in the X-ray part of the spectrum covered by XRT during this bright
state. Rapid variability in soft X-rays has been observed with both the
Swift-XRT and NICER observations with a minimum variability time-scale of 60
and 240 s, and a doubling time-scale of 274 and 1008 s, respectively,
suggesting very compact emitting regions (1.1 $\times$ 10$^{14}$ and 4.0
$\times$ 10$^{14}$ cm). At hard X-rays, a minimum variability time-scale of
$\sim$ 5.5 ks has been observed by NuSTAR. We report the first simultaneous
NICER and NuSTAR observations of BL Lacertae during 2020 October 11-12. The
joint NICER and NuSTAR spectra are well fitted by a broken power law with a
significant difference of the photon index below (2.10) and above (1.60) an
energy break at $\sim$ 2.7 keV, indicating the presence of two different
emission components (i.e, synchrotron and inverse Compton) in the broad band
X-ray spectrum. Leaving the total hydrogen column density toward BL Lacertae
free to vary, a value of N$_{H,tot}$ = (2.58 $\pm$ 0.09) $\times$ 10$^{21}$
cm$^{-2}$ has been estimated.
