This paper reports on the detailed characterisation of the K2-111 planetary system with K2, WASP, and ASAS-SN photometry as well as high-resolution spectroscopic data from HARPS-N and ESPRESSO. The host, K2-111, is confirmed to be a mildly evolved ($\log g=4.17$), iron-poor ([Fe/H]$=-0.46$), but alpha-enhanced ([$\alpha$/Fe]$=0.27$), chromospherically quiet, very old thick disc G2 star. A global fit, performed by using PyORBIT shows that the transiting planet, K2-111b, orbits with a period $Pb=5.3518\pm 0.0004$ d, and has a planet radius of $1.82-0.09+0.11$ R$\oplus$ and a mass of $5.29-0.77+0.76$ M$\oplus$, resulting in a bulk density slightly lower than that of the Earth. The stellar chemical composition and the planet properties are consistent with K2-111b being a terrestrial planet with an iron core mass fraction lower than the Earth. We announce the existence of a second signal in the radial velocity data that we attribute to a non-transiting planet, K2-111c, with an orbital period of $15.6785\pm 0.0064$ days, orbiting in near-3:1 mean-motion resonance with the transiting planet, and a minimum planet mass of $11.3\pm 1.1$ M$\oplus$. Both planet signals are independently detected in the HARPS-N and ESPRESSO data when fitted separately. There are potentially more planets in this resonant system, but more well-sampled data are required to confirm their presence and physical parameters.