The arm length and the isolation in space enable the Laser Interferometer Space Antenna (LISA) to probe for signals unattainable on the ground, opening a window to the subhertz gravitational-wave universe. The coupling of unavoidable angular spacecraft jitter into the longitudinal displacement measurement, an effect known as tilt-to-length (TTL) coupling, is critical for realizing the required sensitivity of picometer/Hz. An ultrastable interferometer test bed has been developed in order to investigate this issue and validate mitigation strategies in a setup representative of LISA and in this paper it is operated in the long-arm interferometer configuration. The test bed is fitted with a flat-top beam generator to simulate the beam received by a LISA spacecraft. We demonstrate a reduction of TTL coupling between this flat-top beam and a Gaussian reference beam via the introduction of two- and four-lens imaging systems. TTL coupling factors below ±25μm/rad for beam tilts within ±300μrad are obtained by careful optimization of the system. Moreover, we show that the additional TTL coupling due to lateral-alignment errors of elements of the imaging system can be compensated by introducing lateral shifts of the detector and vice versa. These findings help validate the suitability of this noise-reduction technique for the LISA long-arm interferometer. © 2020 authors. Published by the American Physical Society.