Context. Low-ionisation, nuclear emission-line region (LINER) nuclei are said to be different from other active galactic nuclei (AGN) due to the presence of complex absorbing structures along the line-of-sight and/or an inefficient mode of accretion onto the supermassive black hole. However, this is still open. Aims: We investigate the broad band X-ray spectrum of NGC 4102, one of the most luminous LINERs in the Swift/BAT survey. Methods: We studied a 80 ks Suzaku spectrum of NGC 4102, together with archival Chandra and Swift/BAT observations. We also studied the optical (3.5 m/TWIN at Calar Alto observatory) and near-infrared (WHT/LIRIS at Observatorio Roque los Muchachos) spectra that were taken at the same time as the Suzaku data. Results: There is strong evidence that NGC 4102 is a Compton-thick AGN, as suggested by the Swift/BAT detected intrinsic continuum and the presence of a strong narrow, neutral FeKα emission line. We have also detected ionised FeXXV emission lines in the Suzaku spectrum of the source. NGC 4102 shows a variable soft excess found at a significantly higher flux state at the time of Suzaku observations when compared to Chandra observations. Finally, a complex structure of absorbers is seen with at least two absorbers besides the Compton-thick one, derived from the X-ray spectral analysis and the optical extinction. Conclusions: All the signatures described in this paper strongly suggest that NGC 4102 is a Compton-thick Type-2 AGN from the X-ray point of view. The "soft excess", the electron scattered continuum component, and the ionised iron emission line might arise from Compton-thin material photoionised by the AGN. From variability and geometrical arguments, this material should be located somewhere between 0.4 and 2 pc away from the nuclear source, inside the torus and perpendicular to the disc. The bolometric luminosity (Lbol = 1.4 × 1043 erg s-1) and accretion rate (ṁEdd = 5.4 × 10-3) are consistent with other low-luminosity AGN. However, the optical and near infrared spectra correspond to that of a LINER source. We suggest that the LINER classification might be due a different spectral energy distribution according to its steeper spectral index.