  The analysis of gravitational wave (GW) datasets is based on the comparison
of measured time series with theoretical templates of the detector's response
to a variety of source parameters. For LISA, the main scientific observables
will be the so-called time-delay interferometry (TDI) combinations, which
suppress the otherwise overwhelming laser noise. Computing the TDI response to
GW involves projecting the GW polarizations onto the LISA constellation arms,
and then combining projections delayed by a multiple of the light propagation
time along the arms. Both computations are difficult to perform efficiently for
generic LISA orbits and GW signals. Various approximations are currently used
in practice, e.g., assuming constant and equal armlengths, which yields
analytical TDI expressions. In this article, we present 'fastlisaresponse', a
new efficient GPU-accelerated code that implements the generic TDI response to
GWs in the time domain. We use it to characterize the parameter-estimation bias
incurred by analyzing loud Galactic-binary signals using the equal-armlength
approximation. We conclude that equal-armlength parameter-estimation codes
should be upgraded to the generic response if they are to achieve optimal
accuracy for high (but reasonable) SNR sources within the actual LISA data.
