  Observations collected with the Atacama Large Millimeter/submillimeter Array
(ALMA) and analysis of broadband X-ray spectra have recently suggested the
presence of a central compact object (CCO) in SN 1987A. However, no direct
evidence of the CCO has been found yet. Here we analyze Chandra X-ray
observations of SN 1987A collected in 2007 and 2018, and synthesize the 2027
Chandra and 2037 Lynx spectra of the faint inner region of SN 1987A. We
estimate the temporal evolution of the upper limits of the intrinsic luminosity
of the putative CCO in three epochs (2018, 2027 and 2037). We find that these
upper limits are higher for higher neutron star (NS) kick velocities due to the
increased absorption from the surrounding cold ejecta. We compare NS cooling
models with both the intrinsic luminosity limits obtained from the X-ray
spectra, and the ALMA constraints with the assumption that the observed blob of
SN 1987A is primarily heated by thermal emission. We find that the synthetic
Lynx spectra are crucial to constrain physical properties of the CCO, which
will be confirmed by future observations in the 2040s. We draw our conclusions
based on two scenarios, namely the non-detection and detection of NS by Lynx.
If the NS is not detected, its kick velocity should be ~700 km/s. Furthermore,
the non-detection of the NS would suggest rapid cooling processes around the
age of 40 years, implying strong crust superfluidity. Conversely, in the case
of NS detection, the mass of the NS envelope must be high.
