We present first-order models for tilt-to-length (TTL) coupling in Laser Interferometer Space Antenna (LISA), both for the individual interferometers, as well as in the time-delay interferometry (TDI) Michelson observables. These models include the noise contributions from angular and lateral jitter coupling of the six test masses, six movable optical subassemblies, and three spacecraft. We briefly discuss which terms are considered to be dominant and reduce the TTL model for the second-generation TDI Michelson X observable to these primary noise contributions to estimate the resulting noise level. We show that the expected TTL noise will initially violate the entire mission displacement noise budget, resulting in the known necessity to fit and subtract TTL noise in data postprocessing. By comparing the noise levels for different assumptions prior to subtraction, we show why noise mitigation by realignment prior to subtraction is favorable. We then discuss that the TTL coupling in the individual interferometers will have noise contributions that will not be present in the TDI observables. Models for TTL coupling noise in TDI and in the individual interferometers are therefore different, and commonly made assumptions are valid as such only for TDI, but not for the individual interferometers. Finally, we analyze what implications can be drawn from the presented models for the subsequent fit-and-subtraction in postprocessing. We show that noise contributions from the test mass and intersatellite interferometers are indistinguishable, such that only the combined coefficients can be fit and used for subtraction. However, a distinction is considered not necessary. Additionally, we show a correlation between coefficients for transmitter and receiver jitter couplings in each individual TDI Michelson observable. This full correlation, however, can be resolved by using all three Michelson observables for fitting the TTL coefficients. Published by the American Physical Society 2024