  This paper presents a theoretical study on the production of the
heavy-flavour decay lepton (HFL) in high-energy nuclear collisions at the LHC.
The pp-baseline is calculated by the FONLL program, which matches the
next-to-leading order pQCD calculation with the next-to-leading-log large-$p_T$
resummation. The in-medium propagation of heavy quarks is driven by the
modified Langevin equations, which consider both the elastic and inelastic
partonic interactions. We propose a method to separate the respective influence
of the five factors, such as pp-spectra, the cold nuclear matter (CNM) effects,
in-medium energy loss (E-loss), fragmentation functions (FFs), and decay
channels, which may contribute to the larger $R_{AA}$ of HFL $\leftarrow b$
compared to that of HFL $\leftarrow c$ in nucleus-nucleus collisions. Based on
quantitative analysis, we demonstrate that different decay channels of charm-
and bottom-hadrons play an important role at $p_T<$5 GeV, while the
mass-dependent E-loss dominates the higher $p_T$ region. It is also found that
the influences of the CNM effects and FFs are insignificant, while different
initial pp-spectra of charm and bottom quarks have a considerable impact at
$p_T>$ 3 GeV. Furthermore, we explore the path-length dependence of jet
quenching by comparing the HFL $R_{AA}$ in two different collision systems. Our
investigations show smaller HFL $R_{AA}$ in Pb+Pb than that in Xe+Xe within the
same centrality bin, which is consistent with the ALICE data. The longer
propagation time and more effective energy loss of heavy quarks in Pb+Pb
collisions play critical roles in the stronger yield suppression of the HFL
compared to that in Xe+Xe. In addition, we observe a scaling behaviour of the
HFL $R_{AA}$ in Xe+Xe and Pb+Pb collisions.
