  Time-delay interferometry (TDI) is a crucial step in the on-ground data
processing pipeline of the Laser Interferometer Space Antenna (LISA), as it
reduces otherwise overwhelming laser noise and allows for the detection of
gravitational waves. This being said, several laser noise couplings have been
identified that limit the performance of TDI. First, on-board processing, which
is used to decimate the sampling rate from tens of MHz down to a few Hz,
requires careful design of the anti-aliasing filters to mitigate folding of
laser noise power into the observation band. Furthermore, the flatness of those
filters is important to limit the effect of the flexing-filtering coupling.
Secondly, the post-processing delays applied in TDI are subject to ranging and
interpolation errors. All of these effects are partially described in the
literature. In this paper, we present them in a unified framework and give a
more complete description of aliased laser noise and the coupling of
interpolation errors. Furthermore, for the first time, we discuss the impact of
laser locking on laser noise residuals in the final TDI output. To verify the
validity of the analytic PSD models we derive, we run numerical simulations
using LISA Instrument and calculate second-generation TDI variables with PyTDI.
We consider a setup with six independent lasers and with locked lasers (locking
configuration N1-12). We find that laser locking indeed affects the laser noise
residual in the TDI combination as it introduces correlations among the six
lasers inducing slight modulations of the PSD compared to the case of six
independent lasers. This implies further studies on laser noise residuals
should consider the various locking configurations to produce accurate results.
