Artículo de publicación ISIContext. LHS 1140 is an M dwarf known to host two transiting planets at orbital periods of 3.77 and 24.7 days. They were detected with HARPS and Spitzer. The external planet (LHS 1140 b) is a rocky super-Earth that is located in the middle of the habitable zone of this low-mass star. All these properties place this system at the forefront of the habitable exoplanet exploration, and it therefore constitutes a relevant case for further astrobiological studies, including atmospheric observations. Aims. We further characterize this system by improving the physical and orbital properties of the known planets, search for additional planetary-mass components in the system, and explore the possibility of co-orbitals. Methods. We collected 113 new high-precision radial velocity observations with ESPRESSO over a 1.5-yr time span with an average photon-noise precision of 1.07 m s−1. We performed an extensive analysis of the HARPS and ESPRESSO datasets and also analyzed them together with the new TESS photometry. We analyzed the Bayesian evidence of several models with different numbers of planets and orbital configurations. Results. We significantly improve our knowledge of the properties of the known planets LHS 1140 b (Pb ~ 24.7 days) and LHS 1140 c (Pc ~ 3.77 days). We determine new masses with a precision of 6% for LHS 1140 b (6.48 ± 0.46 M⊕) and 9% for LHS 1140 c (mc = 1.78 ± 0.17 M⊕). This reduces the uncertainties relative to previously published values by half. Although both planets have Earth-like bulk compositions, the internal structure analysis suggests that LHS 1140 b might be iron-enriched and LHS 1140 c might be a true Earth twin. In both cases, the water content is compatible to a maximum fraction of 10–12% in mass, which is equivalent to a deep ocean layer of 779 ± 650 km for the habitable-zone planet LHS 1140 b. Our results also provide evidence for a new planet candidate in the system (md = 4.8 ± 1.1M⊕) on a 78.9-day orbital period, which is detected through three independent methods. The analysis also allows us to discard other planets above 0.5 M⊕ for periods shorter than 10 days and above 2 M⊕ for periods up to one year. Finally, our co-orbital analysis discards co-orbital planets in the tadpole and horseshoe configurations of LHS 1140 b down to 1 M⊕ with a 95% confidence level (twice better than with the previous HARPS dataset). Indications for a possible co-orbital signal in LHS 1140 c are detected in both radial velocity (alternatively explained by a high eccentricity) and photometric data (alternatively explained by systematics), however. Conclusions. The new precise measurements of the planet properties of the two transiting planets in LHS 1140 as well as the detection of the planet candidate LHS 1140 d make this system a key target for atmospheric studies of rocky worlds at different stellar irradiations.